In the light of almost a century of struggle to make (common) sense of Quantum Mechanics and to reconcile it with General Relativity, it is proposed to (for some time) forget about quantizing gravity or striving for one Theory of Everything or “Weltformel”, which would describe the whole of reality without any joints or suture marks. Instead of one single monolithic formalism, a three-legged compound approach is argued for. Quantum Mechanics, Relativity and Thermodynamics are proposed as the main pillars of reality, each with its well-defined realm, specific features, and clearly marked interfaces between the three of them. Not only classical reality, which is rather directly accessible to us, is then comprehensively modelled by their encompassing combination. Quantum phenomena are understood as undoubtedly lying at the bottom of classical physics and at the same time, they become “fully real” only when embedded in classical frames between preparation and measurement in time. It is then where thermodynamics steps in and provides the mediating glue. The aim of this short contribution is not to deliver novel quantitative results but rather to propose a comprehensive research program and to coarsely lay out a very roughly coherent self-referential sketch starting from the beginning of the one universe, which we inhabit.

Two heating surfaces with longitudinal fins are located within the closed channel inside the housing made of thermal insulation material. The air flow inside the channel was carried out by an axial fan. The heating of the fins is established by using two positive temperature coefficient heating elements (PTC). Air flows circularly from one finned surface to another, and after reaching the required temperature, it leaves the housing. In the heating system conceived in this way, a methodology based on transient thermal irreversibility of heating sources and circular air flow has been established. Volumetric air flow and circulation time within the channel were varied. The total entropy generated does not include hydraulic irreversibility, but transient thermal irreversibility of the air and heat sources. For conducting analytical modeling, the temperature of the PTC heater was considered constant at 423K and 473K. Volumetric air flow varied in the interval from 0.00001m3s-1 to 0.00006m3s-1. The experimental determination of the transient thermal entropy was performed at a much higher air flow rate of 0.005m3s-1 inside the closed channel. Due to the continuous increase in air temperature, the temperatures of both PTC heaters increased within the examined time interval of 300s. According to experimental testing, the total transient thermal entropy of the described heating system has a minimum after 175s from the start of the circular heating of the air. The minimum of transient entropy also implies the optimal time of channel opening and exit of heated air.

In this work, satellite data from the Clouds and Earth’s Radiant Energy System (CERES) and Moderate Resolution Imaging Spectroradiometer (MODIS) instruments is analyzed to determine how the global absorbed sunlight and global entropy generation rate have changed during the time period from 2002 to 2023. The data is used to test hypotheses derived from the Maximum Power Principle (MPP) and Maximum Entropy Production Principle (MEP) about the evolution of earth’s surface and atmosphere. The results indicate that the amount of absorbed sunlight has increased over the last 20 years but rising surface temperatures have caused the entropy generation rate to remain approximately constant despite that decrease in albedo. The results are simpler to explain using the MPP but do not completely rule out the MEP. Given the acceptance of the MPP or MEP, some extensions and nuances are discussed.

Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems—thermal, externally loaded, internally reactive, open and closed––are developed via selection of suitable thermodynamic potentials. Here we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented––and demonstrated on grease degradation, battery charging and discharging, metal fatigue and pump flow––can be used for design, analysis, and support of diagnostic monitoring and optimization.

Living systems must solve the problem of realizing their environment to act appropriately to maintain external relationships and internal order for survival and reproduction. This problem is a biological version of the philosophical enigma of how the self can escape solipsism. This study develops a comprehensive model to solve this adaptation problem. LSs must be composed of material entities that have the property of detecting their external states. The detection of the outside is conceptualized as “cognition,” a related state change that occurs at three levels of nested hierarchy: physical, chemical, and semiotic cognitions. Any entity that cognizes the surroundings is a “cognizer.” The hierarchical extension of cognition to all levels of the world provides a monistic view that only cognizers exist. Semiotic cognition is essential for the emergence and evolution of life. Living systems invented semiotic cognitions based on physical and chemical cognitions to manage the probability distribution of events that occur to them. This study proposes a theoretical model in which semiotic cognition is an adaptive process in which inverse causality operations produce particular internal states as symbols that signify hidden external states. This operation makes the living systems aware of the external world.

Coarse-grained molecular dynamics simulations are employed to investigate spatiotemporal evolution of vesicles (polymersomes) via self-assembly of randomly distributed amphiphilic diblock copolymers in water. Vesiculation pathway consists of several intermediate structures such as spherical/rodlike aggregates, wormlike micelles, lamellae, and cavities. Lamella to vesicle transition occurs at a constant aggregation number and is accompanied by a reduction in the solvent accessible surface area. Simulation predictions are in qualitative agreement with the mechanism of vesicle formation in which the unfavorable hydrophobic interactions between water molecules and polymer segments along the edge of the lamella are eliminated at the expense of gaining curvature energy. However, rod-lamella-vesicle transition is accompanied by an increase in copolymer packing density. Hence, the change in the surface area accompanying vesiculation predicted by the simulations is significantly lower than theoretical estimates. Changes in information entropy, quantified by the expectation of the logarithm of the probability distribution function of the segmental stretch parameter s, defined as the difference between the maximum and instantaneous segmental extension, are statistically insignificant along the vesiculation pathway. For rods, lamellae and polymersomes, s follows a log normal distribution. This is explained based on the configurational dynamics of a single diblock chain in water.

Ransomware attacks have rapidly proliferated, inflicting severe financial damages on businesses and individuals. Machine learning approaches to automate ransomware detection have shown promise but grapple with challenges like limited training data. This study introduces a novel deep learning model for few-shot ransomware classification. The model employs entropy features derived directly from malware binaries coupled with a twin neural network architecture utilizing transfer learning. Tests on over 1000 samples across 11 families demonstrate a weighted F1-score of 85.8\%, surpassing existing methods. The approach mitigates biases in limited training data and preserves intricacies lost in image-based features. It exhibits precise classification capabilities even with sparse samples of new ransomware variants. The research highlights the potential of entropy-driven deep learning to equip defenses against emerging zero-day ransomware strains.

A new utilization of entropy in the context of buckling is presented. The novel concept connecting strain energy and entropy for a pin-ended strut is derived. This concept rationalizes the ranking of buckling modes based on strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of buckling modes that coincide with the measurement of initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for given energy roughly decreases with the inverse square of the mode index. For practical engineering, the study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics.

In this work, an entropy-stable and well-balanced numerical scheme for a one-dimensional blood flow model is presented. Such scheme is obtained from an explicit entropy conservative flux along with a second order discretization of the source term by using centered finite differences. We prove that the scheme is entropy-stable and preserves steady-states solutions. In addition, some numerical examples are included to test the performance of the proposed scheme.

The SARS-CoV-2 virus, causative agent of COVID-19, is known for its genetic diversity. Virus variants of concern (VOCs) as well as variants of interest (VOIs) are classified by the World Health Organization (WHO) according to their potential risk to global health. This study seeks to enhance the identification and classification of such variants by developing a novel bioinformatics criterion centered on the virus's spike protein (SP1), a key player in host cell entry, immune response, and a mutational hotspot. To achieve this, we pioneered a unique phylogenetic algorithm which calculates EIIP-entropy as a distance measure based on the distribution of the Electron-Ion Interaction Potential (EIIP) of amino acids in SP1. This method offers a comprehensive, scalable, and rapid approach to analyze large genomic data sets and predict the impact of specific mutations. This innovative approach provides a robust tool for classifying emergent SARS-CoV-2 variants into potential VOCs or VOIs. It could significantly augment surveillance efforts and understanding of variant characteristics, while also offering potential applicability to the analysis and classification of other emerging viral pathogens and enhancing global readiness against emerging and re-emerging viral pathogens.

Abstract: The high entropy alloy (HEA) of equiatomic composition CrNiFeCoMn and with FCC 11 crystal structure was prepared by either induction melting and additive manufacturing with a se- 12 lective laser melting (SLM) process, starting from mechanically alloyed powders. Unlike induction 13 melting, the as-produced SLM alloy showed fine nitride and Cr-rich s phase precipitates. Mechan- 14 ical spectroscopy measurements were performed on specimens cold worked and/or recrystallized. 15 Young’s modulus values of (140±10) GPa and (90±10) GPa were measured at 300 K for induction 16 melted and SLM samples, respectively. The values increased to (160±10) GPa and (170±10) GPa for 17 recrystallized samples. Damping measurements as a function of temperature showed two peaks 18 which were attributed to dislocations bending and grain boundaries sliding. The peaks were super- 19 posed on a temperature increasing background.

We used the complete set of convex pentagons enabling filing the plane without any overlaps or gaps (including the Marjorie Rice tiles) as generators of Voronoi tessellations. Shannon entropy of the tessellations was calculated. Some of the basic mosaics are flexible and give rise to a diversity of Voronoi tessellations. The Shannon entropy of these tessellations varied in a broad range. Voronoi tessellation, emerging from the basic pentagonal tiling built from hexagons only, was revealed (the Shannon entropy of this tiling is zero). Decagons and hendecagon did not appear in the studied Voronoi diagrams. The most abundant Voronoi tessellations are built from three different kinds of polygons. The most widespread is the combination of pentagons, hexagons and heptagons. The most abundant polygons are pentagons and hexagons. No Voronoi tiling built only of pentagons was registered. Flexible basic pentagonal mosaics give rise to a diversity of Voronoi tessellations, which are characterized by the same symmetry group; however, the coordination number of the vertices is variable. These Voronoi tessellations may be useful for the interpretation of the iso-symmetrical phase transitions.

The article is devoted to solving the problem of searching for universal explainable features that can remain explainable for a wide class of objects and phenomena and become an integral part of Explainable AI (XAI). The study is implemented on the example of an applied problem of early diagnostics of plant stress, using Thermal IR (TIR) and HSI, presented by 8 vegetation indices/channels. Each such index was presented by 5 statistical values. A Single-Layer-Perceptron classifier was used as the main instrument. TIR turned out to be the best of the indices in terms of efficiency in the field and sufficient to detect all 7 key days with 100% accuracy. Our study shows also that there are a number of indices, inluding NDVI, and usual color channels Red, Green, Blue, which are close to TIR possibilities in early plant stress detection with 100% accurasy or near, and can be used for wide class of plants and in different conditions their treatment. The stability of the stress classification in our study was maintained when the training set was reduced up to 10% of the dataset volume. The entropy-like feature of (max-min) for any indices/channels have determined as a leadersheep universal high-level explainable feature for the plant stress detection, which used in interaction with some of other statistical features.

We survey the main results emerging in the rapidly developing field that considers the geometry of thermodynamics and statistical mechanics. Our ideas of stability depend on variational principles – Maximum Entropy together with Least Action (and the isomorphic Least Exertion) – and this stability (invariance in time) indicates the centrality of the geometries of the systems. We explore a variety of examples of the application of thermodynamics in both macro- and micro-systems, and propose that irreversibility is an intrinsic and fundamental property of the physical realm (instead of being merely emergent). Using the concept of complex time, we examine the underlying mathematical unity of quantum mechanics, statistical mechanics, and geometrical thermodynamics. We show how the Planck and Boltzmann constants provide the fundamental quantum units for the phenomenological characteristics of the two Noether-conserved quantities controlling overall thermodynamic behaviour: respectively, energy and entropy production. We discuss the far-reaching isomorphisms (between all of complex time, temperature and the system symmetry) that always exist for Maximum Entropy systems, even as they exhibit either irreversible (dissipative, yet still dynamically stable) or reversible (including stable and static geometries) behaviours.

Deep neural networks (DNNs), founded on the brain's neuronal organization, can extract higher-level features from raw input. However, complex intellect via autonomous decision-making is way beyond current AI design. Here we propose an autonomous AI inspired by the thermodynamic cycle of sensory perception, operating between two information density reservoirs. Stimulus unbalances the high entropy resting state and triggers a thermodynamic cycle. By recovering the initial conditions, self-regulation generates a response while accumulating an orthogonal, holographic potential. The resulting high-density manifold is a stable memory and experience field, which increases future freedom of action via intelligent decision-making.

The effect of Zr addition on the melting temperature of the CoCrFeMnNi High Entropy Alloy (HEA), known as the “Cantor’s Alloy”, is investigated, together with its microstructure, mechan-ical properties and thermo-mechanical recrystallization process. The base and Zr-modified al-loys are obtained by vacuum induction melting of mechanically pre-alloyed powders followed by recrystallization. The alloys were characterized by X-ray diffraction, scanning and transmis-sion electron microscopy, thermal analyses, mechanical spectroscopy and indentation measures. The main advantages of Zr addition are: 1) a fast vacuum induction melting (VIM) process; 2) the lower melting temperature, due to Zr eutectics formation with all the Cantor’s alloy elements; 3) the good chemical alloy homogeneity; 4) the mechanical properties improvement of recrystallized grains with a coherent structure. The crystallographic lattice of both alloys resulted to be FCC. Results demonstrate that the Zr-modified HEA presents a higher recrystallization temperature and smaller grain size after recrystallization with respect to the Cantor’s alloy, with precipita-tion of a coherent second phase which enhance the alloy hardness and strength, while maintaining a good tensile ductility.

The universal Debye – Mayer – Kelly hybrid model was proposed for the description of the heat capacity from 0 K to the melting points of substance within the experimental uncertainty for the first time. To describe the heat capacity, the in-house software on the base of commercial one DELPHI-7 was used with a 95% confidence level. To demonstrate the perfect suitability of this model, a thermodynamic analysis of the heat capacities of the fourth group elements, and some compounds of the A^IIIB^V and A^IIB^VI phases was carried out. It produced good agreement within the experimental uncertainty. There is no a similar model description in literature.The Similarity Method is a convenient and effective tool for critical analysis of the heat capacities of isostructural phases, which was used as an example for diamond-like compounds. Phases with the same sum of the atomic numbers of elements (Z), such as diamond and B_0.5 N_{0.5 (cub)} (Z = 6); pure silicon (Si) and Al_0.5 P_0.5 (Z=14); pure germanium (Ge) and Ga_0.5 As_0.5 (Z = 32)); pure grey tin (alpha-Sn) and In_0.5 Sb_0.5, and Cd_0.5 Te_0.5 (Z = 50) have the same heat capacity experimental values in the solid state. The proposed models can be used to both different binary and multicomponent phases. It helps to standardize the physicochemical constants.

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

As shown earlier, the algorithmic complexity, like Shannon information and Boltzmann entropy, tends to increase in accordance with the general law of complification. However, the algorithmic complexity of most material systems does not reach its maximum, i.e. chaotic state, due to the various laws of nature that create certain structures. The complexity of such structures is very different from the algorithmic complexity, and we intuitively feel that its maximal value should be somewhere between order and chaos. I propose a formula for calculation such structural complexity, which can be called - structuredness. The structuredness of any material system is determined by structures of three main types: stable, dissipative, and post-dissipative. The latter are defined as stable structures created by dissipative ones, directly or indirectly. Post-dissipative structures, as well as stable, can exist for an unlimited time, but at the micro level only, without energy influx. The appearance of such structures leads to the “ratchet” process, which determines the structuregenesis in non-living and, especially, in living systems. This process allows systems with post-dissipative structures to develop in the direction of maximum structuring due to the gradual accumulation of these structures, even when such structuring contradicts the general law of complification.

We write the mutual information between an input speech utterance and its reconstruction by a Code-Excited Linear Prediction (CELP) codec in terms of the mutual information between the input speech and the contributions due to the short term predictor, the adaptive codebook, and the fixed codebook. We then show that a recently introduced quantity, the log ratio of entropy powers, can be used to estimate these mutual informations in terms of bits/sample. A key result is that for many common distributions and for Gaussian autoregressive processes, the entropy powers in the ratio can be replaced by the corresponding minimum mean squared errors. We provide examples of estimating CELP codec performance using the new results and compare to the performance of the AMR codec and other CELP codecs. Similar to rate distortion theory, this method only needs the input source model and the appropriate distortion measure.

The Voronoi entropy is a mathematical tool for quantitative characterization of the orderliness of points distributed on a surface. The tool is useful to study various surface self-assembly processes. We provide the historical background, from Kepler and Descartes to our days, and discuss topological properties of the Voronoi tessellation, upon which the entropy concept is based, and its scaling properties, known as the Lewis and Aboav-Weaire laws. The Voronoi entropy has been successfully applied to recently discovered self-assembled structures, such as patterned micro-porous polymer surfaces obtained by the breath figure method and levitating ordered water micro-droplet clusters.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

A mathematical procedure enabling the transformation of an arbitrary tessellation of a surface into a bi-colored complete graph is introduced. Polygons constituting the tessellation are represented by vertices of the graphs. Vertices of the graphs are connected by two kinds of links/edges, namely, by a green link, when polygons have the same number of sides, and by a red link, when the polygons have a different number of sides. This procedure gives rise to a semi-transitive, complete, bi-colored Ramsey graph. The Ramsey number was established as R_trans (3,3)=5. Shannon entropies of the tessellation and graphs are introduced. Ramsey graphs emerging from random Voronoi and Poisson Line tessellations were investigated. The limits ζ=lim┬(N→∞)⁡〖N_g/N_r 〗, where N is the total number of green and red seeds, N_g and N_r, were found ζ=0.272±0.001 (Voronoi) and ζ= 0.47±0.02 (Poisson Line). The Shannon Entropy for the random Voronoi tessellation was calculated as S= 1.690±0.001 and for the Poisson line tessellation as S =1.265±0.015.

Molecular-scale density fluctuations at equilibrium produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution function. This prediction has been confirmed by computer simulations in different liquid models if the size of the observation volume is not large. The reversible work of cavity creation is exactly linked to the probability of finding zero molecules in a given observation volume. The Gaussian formula for the latter probability is scrutinized to arrive at the enthalpy and entropy changes associated with cavity creation. The reversible work of cavity creation has a purely entropic origin due to the solvent-excluded volume effect produced by the inaccessibility of a given region of the configurational space. The consequent structural reorganization of liquid molecules leads to exactly compensating enthalpy and entropy changes. These results are in line with those obtained in a direct statistical mechanical study by Lee.

We discuss the consequences of the unique symmetry of the de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces the thermal bath for matter. The de Sitter spacetime is invariant under the modified translations, ${\bf r}\rightarrow {\bf r} -e^{Ht}{\bf a}$, where $H$ is the Hubble parameter. For $H\rightarrow 0$, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations ${\bf r}\rightarrow {\bf r} -{\bf a}$. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature $T=H/\pi$, which is twice larger than the Gibbons-Hawking temperature of the cosmological horizon. This temperature does not violate the de Sitter symmetry, and thus does not require the preferred reference frame, as distinct from thermal state of matter, which violates the de Sitter symmetry. This leads to the heat exchange between gravity and matter, and to instability of de Sitter state towards the creation of matter, its further heating, and finally to the decay of the de Sitter state. The temperature $T=H/\pi$ determines different processes in the de Sitter environment, which are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy inside the cosmological horizon. The result reproduces the Gibbons-Hawking area law, which is related to the cosmological horizon, $S_{\rm hor}=4\pi KA$, where $K=1/16\pi G$. This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the $f({\cal R})$ gravity. In this thermodynamics, the Ricci scalar curvature ${\cal R}$ and the effective gravitational coupling, $K$, are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume, and the surface entropy of the cosmological horizon remains the same, but with the gravitational coupling $K=df/d{\cal R}$. Such connection takes place only in the $3+1$ spacetime, where there is the special symmetry due to which the variables $K$ and ${\cal R}$ have the same dimensionality. We also consider the lessons from the de Sitter symmetry for the thermodynamics of black and white holes.

Mexico is a well-known seismically active country, which is primarily affected by several tectonic plate interactions along the southern Pacific coastline and by active structures in the Gulf of Baja California. In this paper we investigate this seismicity in the context of a non-extensive statistical approach based on Tsallis entropy. The analysis is performed using data from the corrected Mexican seismic catalogue provided by the National Seismic Service, spanning a period from January 2000 to October 2023. The Gutenberg-Richter law fitting to the earthquake sub-catalogues for all six regions studied indicates magnitudes of completeness between 3.30 and 3.76. All six regions display values of the entropic index in the range 1.52≲q≲1.61, which are lower than the previously estimated range 1.54≲q≲1.70 using catalogue data from 1988 to 2010. The cause of this discrepancy is certainly due to the use of modern recording devices, which are sensitive enough to detect a larger number of low-magnitude events compared to older instrumentation.

We develop new theory from a broad case-study approach to explore a better understanding of what constitutes knowledge and its value as identifiable to human-machine teams. From past research, this trail of exploration will lead to these initial questions: What is the value of debate in the furtherance of knowledge? Will machines with AI be able to contribute to a debate if we humans cannot define it or determine its value sufficiently for a machine’s understanding, contribution, exploration and identification? Like humans, as teammates, machines must be able to determine with AI what constitutes the usable knowledge that contributes to a team’s success in the field (e.g., testing "knowledge" in the field, identifying new knowledge, using knowledge to develop innovation) or its failure (viz., trouble shooting; identifying weaknesses; discovering vulnerabilities, hiding by deception). It matters not whether a debate is public, private or unexpressed by an individual human or machine agent alone; we speculate in this exploration that the process advances the science of autonomous human-machine teams and assists in interpretable machine learning. We conclude with questions and a speculation: How does a human become aware or express its awareness of knowledge? Can a machine be as expressive as its human teammates? And how does a human-machine teammate become aware that its teammates possess sufficient knowledge to perform a task? We speculate that the structure of “knowledge," once found, is resistant to alternatives (i.e., it is ordered); that its functional utility is generalizable; and that its applications are multifaceted (akin to maximum entropy production). The complexity of the team is taken into consideration in our search for knowledge, which can also be used as an information metric.

Symmetry-breaking is a phenomenon that is observed in various contexts, from the early universe to complex organisms, and is considered a key puzzle in understanding the emergence of life. The presence of enantiomeric amino acids and proteins highlights its critical role. However, the origin of symmetry-breaking has yet to be comprehensively explained, particularly from an energetic standpoint. This article explores a novel approach by considering energy dissipation, specifically lost free energy, as a crucial factor in elucidating symmetry-breaking. Through a thorough thermodynamic analysis applicable to enantiomeric systems at various scales, from elementary particles to aggregated matter like crystals, we present experimental findings that establish a direct correlation between non-equilibrium free energy and energy dissipation during formation processes. Results emphasize the pivotal role of energy dissipation not only as an outcome but as the trigger for symmetry-breaking. This insight suggests that understanding the origins of complex systems, from cells to living beings and the universe itself, requires a lens focused on non-equilibrium processes, ultimately facilitating the formation of non-racemic systems.

The introduction of exoskeletons in the industry has focused on improving worker safety. Exoskeletons have the objective of decreasing the risk of injury or fatigue when performing physically demanding tasks. The exoskeleton’s effects on the muscles is one of the most common focus in the assessments. The present study aims to analyse the muscle interactions generated by using a passive lumbar exoskeleton during load-handling tasks in laboratory conditions with and without an exoskeleton. Electromyographic data of the muscles involved in the task were recorded from twelve participants performing load-handling tasks. Correlation Coefficient, Coherence Coefficient, Mutual Information, and Multivariate Sample Entropy were calculated to determine if there were significant differences in muscle interactions between the two test conditions. Results showed statistically significant differences for all pairs of muscles and indicated that the use of the exoskeleton implied more constant values throughout the exercise. The Directed Conditional Granger Causality was obtained to study the directionality of the interactions, with significant differences in two muscle pairs Gluteus-Quadriceps and Gluteus-Lumbar in the gravity-positive direction in both cases. In conclusion, EMG parameters chosen appear to be appropriate measurements for studying the exoskeleton effects over muscle couplings.

Experimental methodologies for fatigue lifetime prediction are time-intensive and susceptible to environmental variables. While the cohesive zone model is popular for predicting adhesive fatigue lifetime, entropy-based methods have also shown promise. This study aims to provide an understanding of the durability characteristics of CFRP adhesive joints by incorporating an entropy damage model within the context of the finite element method (FEM), examined the effects of different adhesive layer thicknesses on SLS models. As the adhesive layer increased in thickness, DAMAGE VARIABLES initially rose and then declined, peaking at 0.3mm. This finding provides crucial understanding into the stress behavior at the resin-CFRP interface and the resin's fatigue mechanisms.

This paper proposes a reconceptualization of the hierarchical understanding of the human organism, challenging the conventional idea of the supremacy of the nervous system. We argue that symbiotic coexistence and functional interdependence among all systems provide the human body with remarkable resistance to the universal tendency of entropy. We first examine the basis of cellular life, referring to ATP and DNA, essential substances that resist the entropic tendency through complex energy mechanisms. Next, we analyze the collaboration between the body's systems, highlighting the critical role of erythrocytes, which constitute 83.9% of the total cells (24.9 trillion), in the context of energy maintenance and homeostasis. We challenge the conventional view that the nervous system, composed of neurons and glial cells, which together make up 0.6% of the total cells (0.17 trillion), occupies the apex of a biological hierarchy, arguing that the nervous system is merely a component of a broader, interdependent mechanism. Finally, we provide a detailed description of human cellular composition, emphasizing the importance of each cell type in the functional context, thus contributing to the totality of the organism. With this, we present a vigorous appeal for the realization of critical reassessments of fundamental premises in human biology.

The healthy function of the vestibular system (VS) is of vital importance for individuals to carry out their daily activities independently and safely. This study carries out Tsallis entropy (TE)-based analysis on insole force sensor data in order to extract features to differentiate between healthy and VS-diseased individuals. Using a specifically developed algorithm, we detrend the acquired data to examine the fluctuation around the trend curve in order to consider the individual’s walking habit and thus increase the accuracy in diagnosis. It is observed that the TE-value increases for diseased people as an indicator of the problem of maintaining balance. As one of the main contributions of this study, in contrast to studies in the literature that focus on gait dynamics requiring extensive walking time, we directly process the instantaneous pressure values, enabling to reduce the data acquisition period significantly. The extracted feature set is then inputted into fundamental classification algorithms, with the Support-Vector-Machine (SVM) demonstrating the highest performance, achieving an average accuracy of 95%. This study constitutes a significant step of a large project aiming to identify specific VS disease together with its stage. The performance achieved in this study provides a strong motivation to further explore this topic.

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links are considered. Shannon-entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic β-colored convex polygons with m β-sides in the given complete graph. Introduced Shannon entropy is insensitive to the exact shape of the graph, but it is sensitive to the distribution of monochromatic polygons in a given graph. The introduced Shannon Entropies Sα and Sβ are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph, Sβ is, in turn, an average uncertainty to find the red β-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon Entropy is suggested. Various measures quantifying the Shannon Entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon Entropies are discussed.

The entropy and charge distributions have been calculated for a simple model of polyelectrolytes attached to the surface of DNA using a field-theoretic method that includes fluctuations to the lowest one-loop order beyond mean-field theory. Experiments have revealed correlation-driven behavior of DNA in charged solutions, including charge inversion and condensation. In our model, the condensed polyelectrolytes are taken to be doubly charged dimers of length comparable to the distance between sites along the phosphate chains. Within this lattice-gas model, each adsorption site is assumed to have either a vacancy or a positively-charged dimer attached with the dimer oriented either parallel or perpendicular to the double helix DNA chain. We find that the inclusion of the fluctuation terms decreases the entropy by ∼50% in the weak binding regime. There, the bound dimer concentration is low because the dimers are repelled from the DNA molecule, which competes with the chemical potential driving them from the solution to the DNA surface. Surprisingly, this decrease in entropy due to correlations is so significant that it overcompensates for the entropy increase at the mean field level, so that the total entropy is even lower than in the absence of interactions between lattice sites. As a bonus, we present a transparent exposition of the methods used that could be useful to students and others wishing to use this formulation to extend this calculation to more realistic models.

In this review, our goal is to design and test quantum-like algorithms for Artificial Intelligence (AI) in open systems to structure a human-machine team to be able to reach its maximum performance. Unlike the laboratory, in open systems, teams face complexity, uncertainty and conflict. All task domains have complexity levels, some have low, and others high levels. Complexity in this new domain is affected by the environment and the task, which are both affected by uncertainty and conflict. We contrast the individual and interdependence approaches to teams. The traditional and individual approach focuses on building teams and systems by aggregating the best available information for individuals, their thoughts, behaviors and skills. Its concepts are characterized chiefly by one-to-one relations between mind and body, a summation of disembodied individual mental and physical attributes, and degrees of freedom corresponding to the number of members in a team; however, this approach is characterized by the many researchers who have invested in it for almost a century with few effects that can be generalized to human-machine interactions; by the replication crisis of today (e.g., the invalid scales for self-esteem, implicit racism, and honesty); and by its many disembodied concepts. In contrast, our approach is based on the quantum-like nature of interdependence. It allows us to theorize about the bistability of mind and body, but it proposes a measurement problem and a non-factorable nature. Bistability addresses team structure and performance; the measurement problem solves the replication crisis; and the non-factorable aspect of teams reduces the degrees of freedom and the information derivable from teammates to match findings by the National Academies of Science. We begin with a review of the science of teams and a focus on human-machine team research in the laboratory versus the open; justifications for rejecting traditional social science while supporting our approach; a full understand of the complexity of the domain, tasks in the domain, and how teams address both; the mathematics involved; a review of results from our model versus the open field; a discussion of the results; conclusions; and the path forward to successfully advance the science of interdependence and autonomy.

With the rapid development of the economy and the transformation of social contradictions, the economic development model in China has also changed, and a high-quality economic development model has been proposed. This paper uses the entropy method to measure the level of innovation and high-quality economic development in nine prefecture-level cities in Fujian Province from 2011 to 2020, and finds that the overall level shows an increasing trend year by year, but there are obvious regional differences. By constructing a grey correlation degree model, it is found that the innovation subsystem and the high-quality economic development are strongly correlated, the development level of innovation and the subsystem of high-quality economic development are both strongly correlated, the grey correlation degree from high to low is green, coordinated, shared, and livelihood, indicating that innovation has a significant impact on high-quality economic development. Based on the research results, countermeasures and suggestions are proposed to promote the coordinated development of innovation and high-quality economy.

The correlations of seismic noise, recorded during 1997-2022 at 229 stations around the world are investigated. The property of waveforms, known as the Donoho-Johnston threshold, is analyzed, which separates the absolute values of the orthogonal wavelet coefficients into "small" and "large". Network of 50 reference points is considered. For each reference point, a time series with a time step of 1 day is calculated as the median of the values of the DJ index from the 5 nearest stations. For each reference point, the correlations between the values of the DJ index at other reference points are calculated in a sliding time window of 365 days. Average values of the DJ index decrease, which is interpreted as indicators of global seismic hazard increasing. The maximum distances between reference points with strong correlations show an explosive increase after 2011. Bursts in the mean coherences between the length of day (LOD) and the values of the DJ index at the reference points precede the release of seismic energy with a delay of about 530 days. High amplitude of the DJ index response to LOD for the times 2020-2022 was identified, which may forecast a strong earthquake in the second half of 2023.

Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from a sells of equal size which are of a primary importance for decorative arts are reported. The pronounced prevalence of hexagons is inherent for the patterns with an equidistant and non-equidistant distribution of points, when the distance between the seed points is of the same order of magnitude as the distance between the turns of the spiral. Penta- and heptagonal “defected” cells appeared in the Voronoi diagrams due to the finite nature of the pattern. The ordered Voronoi tessellations demonstrating the Voronoi entropy larger than 1.71, reported for the random 2D distribution of points, were revealed. The dependence of the Voronoi entropy on the total number of the seed points located on the Archimedes Spirals is reported. Voronoi tessellations generated by the phyllotaxis-inspired patterns are addressed. The aesthetic attraction of the Voronoi mosaics arising from seed points placed on the Archimedes Spirals is discussed.

Spherically symmetric solution in 4D Einstein--Gauss--Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics (ModLogNED) is found. This solution at infinity possesses the charged black hole Reissner--Nordstr\"{o}m behavior. We study the black hole thermodynamics, entropy, shadow, energy emission rate and quasinormal modes. It was shown that black holes can possess the phase transitions and at some range of event horizon radii black holes are stable. The entropy has the logarithmic correction to the area law. The shadow radii were calculated for variety of parameters. We found that there is a peak of the black hole energy emission rate. The real and imaginary parts of the quasinormal modes frequencies were calculated. The energy conditions of ModLogNED are investigated.

Solidification cracking is a major obstacle when joining dissimilar alloys using additive manufacturing. In this work, location-specific solidification cracking susceptibility has been investigated using an integrated computational materials engineering (ICME) approach for a graded alloy formed by mixing P91 steel and Inconel 740H superalloy. An alloy derived from a mixture of 26 wt.% P91 steel and 74 wt.% Inconel 740H, with high configurational and total entropy, was fabricated using wire-arc additive manufacturing. Microstructure characterization revealed intergranular solidification cracks, which increased in length along with the build height. With inputs from experiments, such as secondary dendrite arm spacing, the DICTRA (diffusion-controlled transformations) module within the Thermo-Calc software was used to model location-specific solidification cracking susceptibility. The top region, with the highest cooling rate, has the highest solidification cracking susceptibility and is in good agreement with the experimentally observed crack length. From Scheil simulations, it was deduced that pronounced segregation of Nb and Cu within the cracks increased the solidification range by suppressing the solidus temperature. The overall solidification cracking susceptibility and freezing range was highest for the 26 wt.% P91 alloy amongst the mixed compositions between P91 steel and 740H superalloy, proving that solidification characteristics play a major role in alloy design for additive manufacturing.

Abstract: The increased penetration of renewables in distribution power systems has motivated researchers to take significant interest in local energy transactions. The major goal of Local Energy Markets (LEM) is to promote the participation of small consumers in energy transactions and providing an opportunity for transactive energy systems. Such energy transactions in LEM are considered as a bi-level optimization problem in which all agents at upper and lower levels try to maximize their profits. But typical bi-level problem is very complex as it is inherently nonlinear, discontinued and strongly NP-hard. So, this article proposes the application of hybridized Cross Entropy Covariance Matrix Adaptation Evolution Strategy (CE-CMAES) to tackle such a complex bi-level problem of LEM. The proposed CE-CMAES secured the 1st rank in Testbed-2 entitled, “Bi-level optimization of end-users’ bidding strategies in local energy markets (LM)” at international competitions on Smart Grid Problems, held at GECCO 2020 and WCCI 2020. CE method is used for global exploration of search space and CMAES is used for local exploitation as its adaptive step-size mechanism prevents its premature convergence. A practical distribution system with renewable energy penetration is considered for simulation. The comparative analysis shows that the overall cost, mean fitness and Ranking Index (R.I) obtained from CE-CMAES are superior to those obtained from the state-of-the-art participated algorithms. Wilcoxon Signed Rank Statistical test also proves that CE-CMAES is statistically different from the tested algorithms.

This study addresses the causal links between external factors and the main hydro-climatic variables. There is a gap in the literature on the description of a complete chain in addressing the structures of direct causal links of solar activity on the terrestrial variables. This is why, the present study uses the extensive facilities of the application of information theory in view of recent advances in different fields. Also, by other methods (e.g. neural networks) first are tested the existence non-linear links of solar-terrestrial influences on hydro-climate system. The results are promising related to the solar impact on terrestrial phenomena which is discriminant in space-time domain. The implications prove robust for determining the causal measure of climate variables under direct solar impact which makes it easier to consider solar activity in climate models, by appropriate parametrizations. This study found that hydro-climatic variables are sensitive to solar impact only for certain frequencies (periods) and these have a coherence with the Solar-Flux only for some lags of the Solar-Flux (in advance).

The logarithmic correction to Bekenshtein$-$Hawking entropy in the framework of 4D Einstein - Gauss - Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore the black hole solution with the spherically symmetric metric. The logarithmic term in the entropy has a structure similar to the entropy correction in the semi-classical Einstein equations which mimics the quantum correction to the area low. The energy emission rate of black holes and energy conditions are studied. The quasinormal modes of a test scalar field are investigated. The gravitational lensing of light around BHs was studied. We calculated the deflection angle for some model parameters.

This paper aims to provide an overall review of degradation, damage evolution and fatigue models in the literature of various engineering materials, mostly metals, and composites.

This paper is our attempt on the basis of physical theory to bring more clarification on the question ``What is life?'' formulated in the well-known book of Schr\"odinger in 1944. According to Schr\"odinger, the main distinguishing feature of biosystem's functioning is the ability to preserve its order structure or, in the mathematical terms, to prevent increasing of entropy. Since any biosystem is fundamentally open, it is natural to use open system's theory. However, Schr\"odinger's analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schr\"odinger should also appeal to the ambiguous notion of negative entropy. We suggest to apply the quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of the classical entropy. We consider a complex biosystem $S$ composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., $S=(S_i).$ We study the following problem: if the composed system $S$ can preserve the ``global order'' in the situation of increase of local disorder and if $S$ can preserve its entropy while some of $S_i$ increase their entropies We show that within quantum information theory the answer is positive. The significant role plays entanglement of the subsystems states. In the absence of entanglement, increasing of local disorder generates disorder increasing in the compound system $S$ (as in the classical regime).

Is it possible to quantify in General Relativity, GR, the entropy generated by supermassive black holes, BHs, during its evaporation time, since the intrinsic Hawking radiation in the infinity that, although insignificant, is important in the effects on the thermal quantum atmosphere?The purpose was to develop a formula that allows us to measure the entropy generated during the evaporation time of different types of BHs of: i. remnant BH of the binary black holes’ merger, BBH: GW150914, GW151226 and LTV151012 detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO), and ii. Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman, and thus quantify in GR the “insignificant” quantum effects involved, in order to contribute to the validity of the generalized second law (GSL) that directly links the laws of black hole mechanics to the ordinary laws of thermodynamics, as a starting point for unifying quantum effects with GR. This formula could have some relationship with the detection of the shadow’s image of the event horizon of a BH.This formula was developed in dimensional analysis, using the constants of nature and the possible evaporation time of a black hole, to quantify the entropy generated during that time. The energy-stress tensor was calculated with the 4 metrics to obtain the material content and apply the proposed formula.The entropy of the evaporation time of BHs proved to be insignificant, its temperature is barely above absolute zero, however, the calculation of this type of entropy allows us to argue about the importance of the quantum effects of Hawking radiation mentioned by authors who have studied the quantum effects with arguments that are fundamentally based on the presence of the surrounding thermal atmosphere of the black hole.

A precise understanding of the genes and associated genomes of SARS-CoV2 is important for various reasons such as discovering origin of the virus and virulence and so on. A thorough descriptive understanding of the SARS-CoV2 genomes and other coronavirus of the beta-coronavirus genus is primarily important. In this article, a set of ten genomes of four CoVs and their associated genes are considered for this present study. A spatial representations of nucleotide bases including purine-pyrimidine representations of the different genes of the corresponding genomes are quantified using Hurst exponent, Shannon entropy and density estimation of different nucleotides including GC content, in order to draw a comparison and contrast among the ten genomes of different types of CoVs which include MERS, SARS-CoV, HKU1 (Human Coronavirus) and associated their genes.

We propose a partial information decomposition based on the newly introduced framework of causal tensors, i.e., multilinear stochastic maps that transform source data into destination data. The innovation that causal tensors introduce is that the framework allows for an exact expression of an indirect association in terms of the constituting, direct associations. This is not possible when expressing associations only in measures like mutual information or transfer entropy. Instead of a priori expressing associations in terms of mutual information or transfer entropy, the a posteriori expression of associations in these terms results in an intuitive definition of a nonnegative and left monotonic redundancy, which also meets the identity property. Our proposed redundancy satisfies the three axioms introduced by Williams and Beer. Symmetry and self-redundancy axioms follow directly from our definition. The data processing inequality ensures that the monotonicity axiom is satisfied. Because causal tensors can describe both mutual information as transfer entropy, the partial information decomposition applies to both measures. Results show that the decomposition closely resembles the decomposition of other another approach that expresses associations in terms of mutual information a posteriori. A negative synergistic term could indicate that there is an unobserved common cause.

Fatigue in any material is a result of continuous irreversible degradation process. Traditionally, fatigue life is predicted by extrapolating experimentally curve fitted empirical models. In the current study, unified mechanics theory is used to predict fatigue life of Ti-6Al-4V under monotonic tensile, compressive and cyclic load conditions. The unified mechanics theory is used to derive constitutive model for fatigue life prediction using a three-dimensional computational model. The proposed analytical and computational models have been used to predict the low cycle fatigue life of Ti-6Al-4V alloys. It is shown that the unified mechanics theory can be used to predict fatigue life of Ti-6Al-4V alloys by using simple predictive models that are based on fundamental equation of the material, which is based on thermodynamics associated with degradation of materials.

Despite their obvious differences, biological systems at different scales tend to exhibit common organizational patterns. Unfortunately, these commonalities are usually obscured by the parcelled terminology employed by various scientific sub-disciplines. To explore these commonalities, this papers a comparative study of diverse applications of the maximum entropy principle, ranging from amino acids up to societies. By presenting these studies under a common language, this paper establishes a unified view over seemingly highly heterogeneous biological scenarios.

We study the existence or absence of non-Shannon inequalities for variables that are related by functional dependencies. Although the power-set on four variables is the smallest Boolean lattice with non-Shannon inequalities there exist lattices with many more variables without non-Shannon inequalities. We search for conditions that excludes the existence of non-Shannon inequalities. It is demonstrated that planar modular lattices cannot have non-Shannon inequalities. The existence of non-Shannon inequalities is related to the question of whether a lattice is isomorphic to a lattice of subgroups of a group.

This paper presents the automation of the thin-layer chromatography technique whose separation and identification of molecules present in a mixture are currently done manually and laboriously [1]. We have therefore found an interest in automating this technique. In this part, the method implemented comprises 2 steps. First we proceeded to the segmentation of the spots obtained on the chromatographic plate. We then developed a program to identify families of molecules such as coumarins, terpenes, tannins, flavonoids, polyphenols, etc. by calculating segmentation parameters such as standard deviation, entropy, average pixel intensity from an algorithm on the matlab software. Finally our results have been compared to the results obtained by the traditional identification technique in laboratories. Some similarity between the two results obtained shows the reliability and the robustness of our technique.

The article analyzes Bernoulli 's binary sequences in representation of empirical events about the distribution of natural resources and population sizes. Considering the event as a nonlinear system, and consisting of two dependent random variables, with memory and probabilities in maximum finite or infinite lengths, constant and equal to ½ for both variables (stationary process). The expressions of the possible trajectories remain constant in sequences that are repeated alternating the presence or absence of one of the variables at each iteration (asymmetric). There are constant oscillations in the event except if the variables X₁ and X₂ are regulated as a function of time Y. It is observed that the variables X₁ and X₂ assume in time T_k → ∞ specific behaviors (geometric variable) that can be used as management tools for random systems. In this way, the article seeks to know from this analyzes, the maximum entropy of information in the system by a theoretical view and how to model resources distribution or containment in the given problem.

The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. The measurements made on the photons shows that light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement. Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. It was found that violation of Bell's inequalities could be trivially calculated and for sets of nonmaximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we visit violation of Bell's inequalities problem with a different approach. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with violation in Bell's inequalities and we make similar comparison of this violation with commonly studied entanglement measures, negativity and relative entropy of entanglement. We show that there are interesting orderings for system states.

It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the ‘probability assumption’ needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann’s Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.

The numerical simulation of entropy generation at mixed natural free and forced convection flow in a square lid-driven cavity filled with an eletrically conducting binary fluids saturated porous media in the presence of a magnetic field is performed in this investigation. Both the top and bottom horizontal walls of the cavity are kept at constant and different temperatures while the left and right vertical walls are adiabatic and insulated. The magnetic field is applied in normal direction to the cavity. The Darcy model, including Brinkman term relative to viscous effects and Forchheimer term due to inertial forces, is used for the momentum equations, and the SIMPLER algorithm, based on the control volume finite-element method approach is used to solve the pressure –velocity coupling. The flow pattern and the heat transfer characteristics inside the cavity are presented in the form of isotherms, streamlines and isentropic lines and average Nusselt number trend. The entropy generation rate is determined for various values of Darcy number (10^-3 ≤ Da ≤ 1) and for a range of Hartmann number (0 ≤ Ha ≤ 10²). This study is limited to Pr = 7 which corresponds to water. It is observed that entropy generation is very affected by the variations of dimensionless control parameters considered.

We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system's lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two non parametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets.

The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible paradigm. However, to date, the essential rationale for and analysis of classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics, and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer's Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.

The state of the grinding wheel in the grinding process directly affects the surface quality of the workpiece. The monitoring of the wear state of the grinding wheel can effectively identify the wear information of the grinding wheel and timely and effectively repair the grinding wheel. In this paper, a multi-sensor fusion precision grinding wheel wear intelligent monitoring system is established for typical difficult-to-machine aerospace material titanium alloy, and a multi-eigenvalue fusion algorithm based on improved support vector machine (SVM) is proposed. The extracted sound emission signal wavelet packet decomposition coefficient mean square value, force signal grinding force ratio, and vibration signal effective value are used as the input of the improved support vector machine, and the identification strategy is adjusted by the entropy weight evaluation method. The results show that the monitoring system established in this paper can effectively identify the wear state of the grinding wheel, and the monitoring accuracy can reach more than 92%

In recent years, due to the detrimental impact of traditional gas-liquid refrigerants on the environment, the pursuit of solid-state refrigeration technology based on elastocaloric effect, as a promising sustainable alternative, has been promoted. However, the traditional trial-and-error method is inefficient and difficult to meet the material application requirements. In this work, machine learning (ML) was employed to accelerate the development of NiTi-based shape memory alloy (SMA) with excellent elastocaloric effect. By means of active learning, we identified 9 novel NiTi-based SMAs in four iterations, the phase transformation-induced entropy change (ΔS) of which are as high as over 90 J/kg·K-1. Moreover, the model exhibits good interpretability, allowing us to understand the relevance between the target and features from the aspect of mechanism.

China's economic development has shifted from high speed to high quality. This study constructs an evaluation index for China’s high-quality development utilizing a new development concept. The entropy method and cluster analysis were used to assess the level of high-quality development in China between 2015 and 2021. Kernel density estimation method was employed to explore spatiotemporal dynamics. The results reveal significant differences in the level of economic development among provinces in China; the eastern region is significantly better than the central, northeastern, and western regions. From the perspective of the sub-item evaluation, challenges with uneven, uncoordinated, and insufficient economic development exist in various Chinese provinces.

The utilization of selective laser melting (SLM) for high entropy alloys (HEAs) holds significant promise in commercial applications, and substantial experimental research efforts have been directed toward this domain. To take advantage of the reported experimental data of SLM manufactured (SLM-ed) HEAs and reduce unnecessary experimentation, this study incorporates machine learning (ML) techniques for the phase and tensile properties prediction of SLM-ed HEAs, thus presenting a novel avenue for accelerating the discovery of new SLM-ed HEAs. Through the adjustment of material descriptors and machine learning models, a model has been developed with an impressive accuracy of 93.8% in distinguishing between face-centered cubic (FCC), body-centered cubic (BCC), and dual-phase (FCC+BCC). Additionally, optimized models have been devised for the prediction of tensile properties, namely ultimate tensile strength (UTS), yield strength (YS), and elongation (δ), achieving noteworthy MAPEs (mean absolute percentage errors) of 10.33%, 8.55%, and 28.48%, respectively. Furthermore, several HEAs were fabricated using SLM, and the experimental outcomes exhibited a favorable alignment with the predicted results. These efforts carry significant implications in advancing the utilization of SLM for HEAs.

This study concerns calculation and comparison of Fe, Co, Ni and Cu deposition rates in tungsten codeposition process based on electrodeposition of numerous tungsten alloys. 8 different tungsten alloys containing from 2 to 5 metals were electrodeposited in constant conditions in order to compare exact reduction rates. Calculated rates enabled control of the alloy composition precise enough to obtain a high-entropy WFeCoNiCu alloy with well-balanced composition. Introduction of copper to form the quinternary alloy was found to catalyze the whole process, increasing deposition rates of all components of the high-entropy alloy.

To enhance the applicability of dual-phase high-entropy alloys (HEAs) like Fe32Cr33Ni29Al3Ti3, fabricated via selective laser melting (SLM), a focus on improving their mechanical properties is essential. As part of this effort, heat treatment was explored. This study compares the microstructure and mechanical properties of the as-printed sample with those cooled in water after undergoing heat treatment at temperatures ranging from 1000 to 1200 ℃ for 1 hour. Both pre- and post-treatment samples reveal a dual-phase microstructure comprising FCC and BCC phases. Although heat treatment led to a reduction in tensile and yield strength, it significantly increased ductility compared to the as-printed sample. This strength-ductility trade-off is related to changes in grain sizes with ultrafine grains enhancing strength and micron grains optimizing ductility, also the influence of the content of FCC/BCC phases and dislocation density. In particular, the sample heat-treated at 1000 °C for 1 hour and then water-cooled exhibited a better combination of strength and ductility, a yield strength of 790 MPa, and an elongation of 13%. This research offers innovative perspectives on crafting dual-phase HEA of Fe32Cr33Ni29Al3Ti3, allowing for tailorable microstructure and mechanical properties through a synergistic approach involving SLM and heat treatment.

A formulation of the Density Functional Theory (DFT) is constructed as an application of the method of maximum entropy for an inhomogeneous fluid in thermal equilibrium. The use of entropy as a systematic method to generate optimal approximations is extended from the classical to the quantum domain. This process introduces a family of trial density operators that are parametrized by the particle density. The optimal density operator is that which maximizes the quantum entropy relative to the exact canonical density operator. This approach reproduces the variational principle of DFT and allows a simple proof of the Hohenberg-Kohn theorem at finite temperature. Finally, as an illustration, we discuss the Kohn-Sham approximation scheme at finite temperature

The increase in ecosystem biodiversity can be perceived as one of the universal processes converting energy into information across a wide range of living systems. This study delves into the dynamics of living systems, highlighting the distinction between ex-post adaptation, typically associated with natural selection, and its proactive counterpart, ex-ante adaptability. Through coalescence experiments using synthetic ecosystems, we (i) quantified an ecosystem stability, (ii) identified correlations between species richness and the stability, (iii) proposed a mechanism for increasing biodiversity through moderate inter-ecosystem interactions, and (iv) inferred that the information carrier of ecosystems is species composition, or merged genomic information. Additionally, we observed that (v) changes in ecosystems are constrained to a low-dimensional state space, with three distinct alteration trajectories—fluctuations, rapid environmental responses, and long-term changes—converging into this state space in common. These findings suggest that daily fluctuations may predict broader ecosystem changes. Our experimental insights, coupled with an exploration of living systems' information dynamics from an ecosystem perspective, enhance our predictive capabilities for natural ecosystem behavior, providing a universal framework for understanding a broad spectrum of living systems.

In this paper, we consider the one-dimensional Ising model (shortly, 1D-MSIM) having mixed spin-(s,(2t−1)/2) with nearest neighbors and the external magnetic field. We establish the partition function of the model by means of the transfer matrix. Under a null boundary condition, we compute certain thermodynamic quantities for the 1D-MSIM. We find some precise formulas to determine the model’s free energy, entropy, magnetization, and susceptibility. By examining the model’s associated iterative equations, we use the cavity approach to investigate the phase transition problem. We numerically determine the model’s periodicity.

In this study, our primary objective was to analyze the tradeoff between accuracy and complexity in machine learning models, with a specific focus on the impact of reducing complexity and entropy on the production of landslide susceptibility maps. We aimed to investigate how simplifying the model and reducing entropy can affect the capture of complex patterns in the susceptibility maps. To achieve this, we conducted a comprehensive evaluation of various machine-learning algorithms for classification tasks. We compared the performance of these algorithms in terms of accuracy and complexity, considering both "before" and "after" scenarios of dimensionality reduction using Principal Component Analysis (PCA). Our findings revealed that reducing complexity and lowering entropy can lead to an increase in model accuracy. However, we also observed that this reduction in complexity comes at the cost of losing important complex patterns in the produced landslide susceptibility maps. By simplifying the model and reducing entropy, certain intricate relationships and uncertain patterns may be overlooked, resulting in a loss of information and potentially compromising the accuracy of the susceptibility maps. The analysis encompassed a diverse range of machine learning algorithms, including Random Forest (RF), Extra Trees (EXT), XGboost, LightGBM, Catboost, Naive Bayes (NB), K-Nearest Neighbors (KNN), Gradient Boosting Machine (GBM), and Decision Trees (DT). Each algorithm was evaluated for its strengths and limitations, considering the tradeoff between accuracy and complexity. Before dimensionality reduction, the algorithms demonstrated promising results, with RF exhibiting excellent AUC/ROC scores and average accuracy. However, computational costs were noted as a potential drawback for RF, especially when dealing with large datasets. EXT showcased robust performance and good accuracy, while XGboost demonstrated its ability to handle complex relationships within large datasets, albeit requiring careful hyperparameter tuning. The efficiency and scalability of LightGBM made it a suitable choice for large datasets, although it displayed sensitivity to class imbalance. Catboost excelled in handling categorical features, but longer training times were observed for larger datasets. NB showcased simplicity and computational efficiency but assumed independence among features. KNN, known for its capability to capture local patterns and spatial relationships, was found to be sensitive to the choice of distance metric. GBM, while capturing complex relationships effectively, was prone to overfitting without proper regularization. DT, with its interpretability and ease of understanding, faced limitations in terms of overfitting and limited generalization. After dimensionality reduction, certain algorithms exhibited improvements in their AUC/ROC scores and average accuracy, including RF, EXT, XGboost, and LightGBM. However, for a few algorithms, such as NB and DT, a decrease in performance was observed. This study provides valuable insights into the performance characteristics, strengths, and limitations of various machine learning algorithms in classification tasks. Researchers and practitioners can utilize these findings to make informed decisions when selecting algorithms for their specific datasets and requirements. We also aim to identify the potential factors contributing to the high accuracy rates obtained from these ensembled algorithms and explore possible shortcomings of non-ensembled algorithms that may result in lower accuracy rates. By conducting a comprehensive analysis of these algorithms, we seek to provide valuable insights into the benefits and limitations of ensembled approaches for landslide susceptibility mapping. Our study sheds light on the challenges faced when balancing accuracy and complexity in machine learning models for landslide susceptibility mapping. It emphasizes the importance of carefully considering the level of complexity and entropy reduction in relation to the specific patterns and uncertainties present in the data. By providing insights into this tradeoff, our research aims to assist researchers and practitioners in making informed decisions regarding model complexity and entropy reduction, ultimately improving the quality and interpretability of landslide susceptibility maps.

Conservation of tropical endemic amphibians largely suffers from Wallacean shortfall, a gap to which predictive species distribution models have contributed significantly to bridge by delineating probable distribution and the underlying suitable habitat within their distributional range. However, rarely is a prediction model ground-truthed to evaluate their predictive performance. Here we present a species distribution modeling approach using maximum entropy algorithm corrected for smaller sample size, in guiding explorative surveys aimed at optimizing survey effort and discovering unrecorded populations of Zhangixalus suffry, a rhacophorid tree-frog endemic to the northeastern part of the Indian subcontinent along with the factors limiting their distribution. With only 16 established historical locality data to model for (after spatial thinning to reduce autocorrelation) and a set of environmental predictors (climatic, topographic, and landscape composition), our model prediction enabled the successful discovery of seven new population records from unreported landscapes, extending its southernmost distributional limit over a considerable distance. The final composite distribution model combining all the locality records (n=23) predicted similar core areas of suitable habitat consistent with the known geographic distribution of the species but showed poor representation under existing coverage of Protected Area (PA) network in the Region with only 7% representation of suitable habitat under protection. Habitat suitability of a site was significantly governed by factors related to precipitation (precipitation seasonality and precipitation of the warmest quarter) and topographic factors that can influence it (elevation and aspect). This corroborates with the known ecology of Rhacophorid frogs, especially concerning their seasonal explosive reproductive strategy and foam nest-building behavior.Through this study, we propose explorative surveys guided by species distribution models to expedite unknown population discovery of rare, tropical endemic amphibians and using such taxa as surrogates in identifying conservation priority zones that can be directly applied to reserve design and conservation and management planning.

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black holes under the generalized Brans-Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius~$r_+$~is small, the effect of the entropy correction term on the entropy is very obvious, while for larger values~$r_+$~, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of the geodesic motion of particles in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyzes the dependence of the innermost stable circular orbit on model parameters. Also, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, the specific energy and angular momentum of the particles which move in circular orbits.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

In the perspective of designing complex concentrated alloys (CCAs) for structural applications, sigma (σ) phase is important. It is generally known to be an embrittling phase leading to a degradation in the mechanical properties of CCAs. This necessitates detailed investigations on the evolution of σ phase in these alloys. In the present study, an equiatomic CoCrCuMnNi CCA is chosen, in which σ phase appears at 800°C, as reported in a recent publication [1]. To this end, the present investigation aims at understanding the evolution of this phase so that its presence can be controlled for the purpose of preventing degradation in mechanical properties. In the present work, a vacuum arc melted alloy, after homogenisation (at 400°C for 5h), is heat-treated for different times ranging from 1 to 9h at 800°C followed by water quenching. Extensive characterisation has been carried out using X-Ray Diffraction (XRD) and Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) techniques to understand the sequence of σ phase precipitation at 800°C.

This present work explores the performance of a thermal-magnetic engine of Otto type, considering as a working substance an effective interacting spin model corresponding to the q− state clock model. We obtain all the thermodynamic quantities for the q = 2, 4, 6, 8 cases in a small lattice size (3×3 with free boundary conditions) by using the exact partition function calculated from the energies of all the accessible microstates of the system. The extension to bigger lattices was performed using the mean-field approximation. Our results indicate that the total work extraction of the cycle is highest for the q=4 case, while the performance for the Ising model (q=2) is the lowest of all cases studied. These results are strongly linked with the phase diagram of the working substance and the location of the cycle in the different magnetic phases present, where we find that the transition from a ferromagnetic to a paramagnetic phase extracts more work than one of the Berezinskii–Kosterlitz–Thouless to paramagnetic type. Additionally, as the size of the lattice increases, the extraction work is lower than smaller lattices for all values of q presented in this study.

High-entropy alloys (HEAs) are of great interest in the field of materials science and engineering. Unlike conventional alloys, which contain a maximum of two base metals, this new category of materials consists of multi-principle elements and the possible number of alloy compositions, in case of HEAs, is outstandingly higher than that for conventional alloys. Here, a review on the high-entropy alloys, has been provided, on the issue whether the earliest definition of High- Entropy alloys, proposed in 2004^{[2, 4]}, is consistent with one of the four-component equiatomic Compositionally complex alloys exhibiting a “High-entropy” effect.

Diagnostics and decomposition of atmospheric disturbances in a planar flow are considered and applied to numerical modeling results with the direct possibility to use in atmosphere monitoring especially in such strong events which follow magnetic storms. The study examines a situation in which the stationary equilibrium temperature of a gas may depend on a vertical coordinate, that seriously complicates the problem solution. The relations connecting perturbations for acoustic and entropy modes are analytically established and led to the solvable diagnostic equations. These perturbation structures, found as the equation solutions specify acoustic and entropy modes in an arbitrary stratified gas under the condition of stability. These time-independent diagnostic relations link gas perturbation variables of the acoustic and the entropy modes. Hence, they provide the ability to decompose the total vector of perturbations into acoustic and non-acoustic (entropy) parts uniquely at any instant within the all accessible heights range. As a prospective model, we consider the diagnostics at the height interval [120;180] km, where the equilibrium temperature of a gas depends linearly on the vertical coordinate. For such a heights range it is possible to proceed with analytical expressions for pressure and entropy perturbations of gas variables. Individual profiles of acoustic and entropy parts for some data, obtained by numerical experiment, are illustrated by the plots for the pure numerical data against ones obtained by the model. The total energy of a flow is determined for both approaches and its height profiles are compared.

The anisotropy in the CMBR detected by the COBE satellite has sprouted the research and theories of the void that got created, after being washed away by a parallel universe after its collision. This details of the roadmap to the parallel universe, that are previously been entangled, but now, separated, with the concept of 2-time dimensions as a time curve of containing the closed curves embedded on the surface area, thereby time running backward in orientation in the parallel universe, along with the perspective of eternal inflation and divided subspaces giving birth to twin universes are provided here. This time curve being responsible for creating an exponentiality of time frames, growing in layers, giving us the perception of the confabulations being an indication of the previously connected worlds.

We derive time evolution equations, namely the Schrodinger-like equations and the Klein-Gordon equations for coherent fi elds and the Kadanoff-Baym (KB) equations for quantum fluctuations, in Quantum Electrodynamics (QED) with electric dipoles in 2 + 1 dimensions. Next we introduce a kinetic entropy current based on the KB equations in the 1st order of the gradient expansion. We show the H-theorem for the Leading-Order self-energy in the coupling expansion (the Hartree-Fock approximation). We show a conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to Quantum Brain Dynamics, that is QED with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain.

Bello's stochastic linear time-varying system theory has been widely used in the wireless communications literature to characterize multipath fading channel statistics. In the context of radar backscatter, this formulation allows for statistical characterization of distributed radar targets in range and Doppler using wide-sense stationary uncorrelated scattering (WSSUS) models. WSSUS models separate the channel from the effect of the waveform and receive filter, making it an ideal formulation for waveform design problems. Of particular interest in the radar waveform design community is the ability to suppress unwanted backscatter from the earth's surface, known as clutter. Various methods for estimating WSSUS system functions have been studied in the literature, but to date, no analytic expressions for radar surface clutter range-Doppler scattering functions exist. In this work we derive a wideband generalization of the Jakes Doppler spectrum model, which is widely used in the wireless communications literature, adapt it for use in radar problems, and show how the maximum entropy method can be used to extend this model to account for internal clutter motion. Validation of the spectral and stationarity properties of the proposed model against a subset of the Australian Ingara sea clutter database is performed, and good agreement is shown.

The Maximum Entropy Theory of Ecology, or METE, is a theoretical framework of macroecology that makes a variety of realistic ecological predictions about how species richness, abundance of species, metabolic rate distributions, and spatial aggregation of species interrelate in a given region. In the METE framework, "ecological state variables" (representing total area, total species richness, total abundance, and total metabolic energy) describe macroecological properties of an ecosystem. METE incorporates these state variables into constraints on underlying probability distributions. The method of Lagrange multipliers and maximization of information entropy (MaxEnt) lead to predicted functional forms of distributions of interest. We demonstrate how information entropy is maximized for the general case of a distribution, which has empirical information that provides constraints on the overall predictions. We then show how METE’s two core functions are derived. These functions, called the "Spatial Structure Function" and the "Ecosystem Structure Function" are the core pieces of the theory, from which all the predictions of METE follow (including the Species Area Distribution, the Species Abundance Distribution, and various metabolic distributions). Primarily, we consider the discrete distributions predicted by METE.We also explore the parameter space defined by the METE’s state variables and Lagrange multipliers. We aim to provide a comprehensive resource for ecologists who want to understand the derivations and assumptions of basic mathematical structure of METE.

The continuous energy transformation processes in heating, ventilation and air conditioning systems of buildings are responsible for 36% of global final energy consumption. Tighter thermal insulation requirements for buildings have significantly reduced heat transfer losses. Unfortunately, this has little effect on energy demand for ventilation. On the basis of the First and the Second Law of Thermodynamics, the concepts of entropy and exergy are applied to the analysis of ventilation air handling unit (AHU) with a heat pump in this paper. This study aims to develop a consistent approach for this purpose, taking into account the variations of reference temperature and temperatures of working fluids. An analytical investigation on entropy generation and exergy analysis are used, when exergy is determined by calculating coenthalpies and evaluating exergy flows and their directions. The results show that each component of the AHU has its individual character of generated entropy, destroyed exergy and exergy efficiency variation. However, the evaporator of heat pump and fans have unabated quantities of exergy destruction. The exergy efficiency of AHU decreases from 45-55% to 12-15% when outdoor air temperature is within the range of –30°C…+10°C, respectively. This helps to determine conditions and components of improving the exergy efficiency of the AHU at variable real-world local climate conditions. The presented methodological approach could be used in the dynamic modelling software and contribute to a wider application of the Second Law of Thermodynamics in practice.

Confidence interval of is an interval corresponding to a specified confidence and including the true value. It can be used to describe the precision of a statistical quantity and quantify its uncertainty. Although the principle of maximum entropy (POME) has been used for a variety of applications in hydrology, the confidence intervals of the POME quantile estimators have not been available. In this study, the calculation formulas of asymptotic variances and confidence intervals of quantiles based on POME for Gamma, Pearson type 3 (P3) and Extreme value type 1 (EV1) distributions were derived. Monte Carlo Simulation experiments were performed to evaluate the performance of derived formulas for finite samples. Using four data sets for annual precipitation at the Weihe River basin in China, the derived formulas were applied for calculating the variances and confidence intervals of precipitation quantiles for different return periods and the results were compared with those of the methods of moments (MOM) and of maximum likelihood (ML) method. It is shown that POME yields the smallest standard errors and the narrowest confidence intervals of quantile estimators among the three methods, and can reduce the uncertainty of quantile estimators

We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon -- a device that interacts with a memory register (a stream of bits), a thermal reservoir (an ideal gas) and a work reservoir (a mass that can be lifted or lowered). Our device is similar to one that we have briefly described elsewhere [1], but it has the additional feature that it can be programmed to recognize a chosen reference sequence, for instance, the binary representation of $\pi$. If the bits in the memory register match those of the reference sequence, then the device extracts heat from the thermal reservoir and converts it into work to lift a small mass. Conversely, the device can operate as a generalized Landauer's eraser (or copier), harnessing the energy of a dropping mass to write the chosen reference sequence onto the memory register, replacing whatever information may previously have been stored there. Our model can be interpreted either as a machine that autonomously performs a conversion between information and energy, or else as a feedback-controlled device that is operated by an external agent. We derive generalized second laws of thermodynamics for both pictures. We illustrate our model with numerical simulations, as well as analytical calculations in a particular, exactly solvable limit.

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of both observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the tranverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsytem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.

The value of an NBA basketball player varies at each crucial point in time, depending on the player’s career and performance. This study constructs a player’s value assessment model. The model comprises two parts. First, from an objective perspective, entropy is employed to measure each player’s achievement in five categories—rebounds, assists, steals, blocked shots, and scores. The total entropy assessment value is calculated and then combined with the players’ scores to develop a player's value matrix to assess the relative value model among players of the same type.

Flash flood is one of the most significant natural disasters in China, particularly in mountainous area, causing heavy economic damage and casualties of life. Accurate risk assessment is critical to an efficient flash flood management. There are more than 530,000 small watersheds in 2058 counties in China where flash flood should be prevented. In practice, with limited fund and different risk levels, the priorities of each small watershed for flash flood prevention and control are also needed for an efficient flash flood management. This paper, take Licheng county in China as an example, aims to give out these priorities for management. First, sensitive indexes are identified among index system, which includes 9 indexes based on underlying surface characteristics of small watershed in hilly region. Second, the range of each index and the rank division of each index for evaluation are determined. Based on the rank divisions for evaluation, the flash flood risk grade eigenvalue (H) is calculated by Variable Fuzzy Method (VFM ) using 1000 samplings generated by Latin hypercube sampling method. Third, the key sensitivity factors that affect flash flood risk grade eigenvalue (H) are assessed by two different global sensitivity analysis methods -- stepwise regression analysis and mutual entropy. Both results indicate that watershed slope (S) is the most sensitive factor; the second is antecedent precipitation index (CN); while other factors are slightly different sensitive in sequence. This study shows that stepwise regression analysis and mutual information analysis are appropriate for the sensitivity analysis of mountain flash flood risk. Finally, based on watershed slope (S), the priorities of flash flood prevention and control of 119 small watersheds in Licheng county are given out.

Iterated games, in which the same economic interaction is repeatedly played between the same agents, are an important framework for understanding the effectiveness of strategic choices over time. To date very little work has applied information theory to the information sets used by agents in order to decide what action to take next in such strategic situations. This article looks at the mutual information between previous game states and an agent's next action by introducing two new classes of games: ’invertible games’ and ‘cyclical games'. By explicitly expanding out the mutual information between past states and the next action we show under what circumstances these expressions can be simplified. These information measures are then applied to the Traveler's Dilemma game and the Prisoner's Dilemma game, the Prisoner's Dilemma being invertible, to illustrate their use. In the Prisoner's Dilemma a novel connection is made between the computational principles of logic gates and both the structure of games and the agents' decision strategies. This approach is applied to the cyclical game Matching Pennies to analyse the foundations of a behavioural ambiguity between two well studied strategies: ‘Tit-for-Tat' and ’Win-Stay, Lose-Switch'.

The present work investigates primarily the morphology evolution of the body-centered-cubic (BCC)/B2 phases in AlxNiCoFeCr high-entropy alloys (HEAs) with increasing Al content, which has been neglected so far. There exist two types of microscopic morphologies of BCC and B2 phases in this HEA series: one is the weave-like morphology induced by the spinodal decomposition, and the other is the microstructure of a spherical disordered BCC precipitation on the ordered B2 matrix that appears in HEAs with a much higher Al content. The shape of coherent precipitates is found to be closely related to the lattice misfit between BCC and B2 phases, which is sensitive to Al. The mechanical properties, including the compressive yielding strength and microhardness of the AlxNiCoFeCr HEAs, are also discussed in light of the concept of the valence electron concentration (VEC).

In this paper, we introduce generalized entropy, the acceleration of its entropy and its the partial entropy. We assume that generalized entropy can be expressed as a second-order polynomial by applying the idea of logistics function to its entropy. In other words, we assume that the acceleration of generalized entropy is a constant. Besides, we show that the negative inverse of the partial entropy can express Newton's classical gravity, which is an inverse square law. By applying these concepts, we attempt to explain that 1) Gravity is constant within small distances with some conditions. It is possible that gravity have 6-states within small distance. Furthermore, within small distance, we show the possibility that the gravitational potential and the Coulomb potential can be treated in the same way, that 2) The rotation speed of a galaxy does not depend on its radius if the radius is within the size level of the universe. (The galaxy rotation curve problem), and that 3) The gravitational acceleration toward the center changes at long distances compared to the classical theory of gravity. Furthermore, we show that the possibility of the existence of some constants which controls gravity and the speed of galaxies, and that gravity may relate on entropy.

General derivation of the well-known Ren-Otsuka relation, 1/α (dTo)/dx=-α/β (where To, x, α and β(>0) are the transformation temperature, the composition, as well as the composition and temperature coefficient of the critical shear constant, c’, respectively) for shape memory alloys, SMAs, is provided based on the similarity of interatomic potentials in the framework of dimensional analysis. A new dimensionless variable, to(x)=(To (x))/(Tm (x) ), describing the phonon softening (where Tm is the melting point) is introduced. The dimensionless values of the heat of transformation, H, and entropy, S as well as the elastic constants c’, c44, A=c44/c' are universal functions of to(x) and have the same constant values at to(0) within sub-classes of host SMAs having the same type of crystal symmetry change during martensitic transformation. The ratio of (dto)/dx and α has the same constant value for all members of a given sub-class and relative increase of c’ with increasing composition should be compensated by the same decrease of to. In the generalized Ren-Otsuka relation the anisotropy factor, A appears instead of c’ and α as well as β are the differences of the corresponding coefficients for the c44 and c’ elastic constants. The obtained linear relation between h and to rationalizes the observed empirical linear relations between the heat of transformation measured by DSC (QAM) and the martensite start temperature, Ms.

This paper addresses the mixed convective flow and heat transfer in combustible third grade fluid through a slant channel that is filled with a permeable materials. The fluid layer in contact with the lower plate is exposed to convective heating with the ambient while at the upper plate, a constant heat flux is experienced. We employ the spectral quasilinearisation method (SQLM) to the coupled nonlinear flow governing equations. Fluid velocity and temperature profiles, local entropy generation and irreversibility ratio are computed and analysed quantitatively and qualitatively. A residual error analysis demonstrated high accuracy and convergence of the numerical method. The results on flow and thermal effects, entropy generation rate and Bejan number revealed fascinating manifestations that have profound implications in design of thermo-mechanical systems. In particular, the results of the thermal analysis are pertinent to optimal designs of systems that achieve efficient energy utilization.

Variability is the predisposition of the elements in systems to assume different values over time and space. In biology, the variability is basic to explain differences and development in organisms but in the fields of scientific and technological information, the effects of variability on evolutionary dynamics of disciplines and technologies are unknown. In a broad analogy with the principles of biology, the variability within research fields can be a central argument to explain trajectories in scientific development and technological evolution. The purpose of the present study is to see whether statistical evidence supports the general hypothesis that the rate of growth in technologies can be explained by the level of variability in scientific fields and with this principal goal to analyze the relation between scientific variability and rate of growth in technologies. Proposed hypothesis of scientific variability here endeavors to explain basic sources of scientific development and technological evolution to lay the foundations for a general theory. The test here is based on emerging research fields of quantum technologies: Quantum Imaging, Quantum Meteorology, Quantum Sensing and Quantum Optics. A preliminary statistical evidence seems in general to support the hypothesis stated that the rate of growth in technological fields can be explained by the level of scientific variability in research fields, measured with relative entropy index. Nonparametric correlation based on Spearman’s rho shows a positive coefficient of 0.80 of these variables; linear model of the rate of technological growth = f(scientific variability) reveals a coefficient of regression equal to 1.63 (R²=0.60). Findings here suggest a general law that scientific variability positively drives scientific development and technological evolution. In particular, a higher variability within research fields can support scientific development and a high rate of growth in technological evolution (measured with scientific and technological information). Proposed hypothesis of scientific variability is especially relevant in environments of rapid change to explain determinants and dynamics of technological change within a general theoretical framework that supports technological management and forecasting of promising innovations.

The physical roots, interpretation, controversies and precise meaning of the Landauer Principle are surveyed. Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It states that an irreversible change in information stored in a computer, such as merging two computational paths, dissipates a minimum amount of heat kBTln2 per a bit of information to its surrounding. The Landauer Principle is discussed in the context of fundamental physical limiting principles, such as the Abbe diffraction limit, the Margolus-Levitin limit and the Bekenstein limit. Synthesis of the Landauer bound with the Abbe, Margolus-Levitin limit and Bekenstein limits yields the minimal time of computation, which scales as τmin~hkBT. Decrease in a temperature of a thermal bath will decrease the energy consumption of a single computation, but, in parallel, it will slow the computation. The Landauer principle bridges between John Archibald Wheeler “it from bit” paradigm and thermodynamics. Experimental verifications of the Landauer Principle are surveyed. Interrelation between thermodynamic and logical irreversibility is addressed. Generalization of the Landauer principle to the quantum and non-equilibrium systems is addressed. Landauer Principle represents the powerful heuristic principle bridging the physics, information theory and computer engineering.

In the century and a half since Maxwell first conjured his “finite being” which Lord Kelvin subsequently dubbed a “daemon”, researchers have explored the connections between non-equilibrium thermodynamics, entropy, and information theory. In recent years various Thermodynamic Uncertainty Relations (TURs) have been derived to inform upon the relationship between the entropy production and the precision possible in thermodynamic machines and processes. In this paper the recently derived TURs are applied to the hypothetical thermodynamic economy as described by Parker [1]. The TURs define the lower bound on the total entropy production of the economy. Changes in this entropy production rate has consequences on the stability of the economic system and plays a central role in the business cycle. This new perspective has important implications for policy makers, researchers, and other economic actors.

Detecting gear rim fatigue cracks using vibration signal analysis is often a challenging task, which typically requires a series of signal processing steps to detect and enhance fault features. This task becomes even harder in helicopter planetary gearboxes due to the complex interactions between different gear sets, and the presence of vibration from sources other than the planetary gear set. In this paper, we propose an effectual processing algorithm to isolate and enhance rim crack features and to trend crack growth in planet gears. The algorithm is based on using cepstrum editing (or liftering) of the hunting tooth synchronous averaged signals (angular domain) to extract harmonics and sidebands of the planet gears, and low-pass filtering and minimum entropy deconvolution (MED) to enhance extracted fault features. The algorithm has been successfully applied to a vibration dataset collected from a planet gear rim crack propagation test undertaken in the Helicopter Transmission Test Facility (HTTF) at DSTG Melbourne. In this test, a seeded notch generated by an electric discharge machine (EDM) was used to initiate a fatigue crack that propagated through the gear rim body over 94 load cycles. The proposed algorithm demonstrated a successful isolation of incipient fault features and provided a reliable trending capability to monitor crack progression. Results of a comparative analysis showed that the proposed algorithm outperformed the traditional signal processing approach.

An overview of the link between nonequilibrium thermodynamics and complexity theory is offered. It is shown how the rate of entropy production can be quantified through the spectrum of the Lyapunov exponents. It was shown how the entropy production per unit of time meets the necessary and sufficient conditions to be a Lyapunov function and constitutes per se an extremal principle. The entropy production fractal dimension conjecture was established. It is shown how the rate of entropy production as a non-extremal criterion represents an alternative way of sensitivity analysis of differential equations. Finally, an extension to biophysical-chemical systems, on the one hand, the use of the dissipation function is shown, as a thermodynamic potential out of equilibrium, in the characterization of biological phase transitions. On the other hand, it was evidenced how the rate of entropy production represents a physical quantity to evaluate the complexity and robustness of cancer.

The performance of bearings plays a pivotal role in determining the dependability and security of rotating machinery. In intricate systems demanding exceptional reliability and safety, the ability to accurately forecast fault occurrences during operation holds profound significance. Such predictions serve as invaluable guides for crafting well-considered reliability strategies and executing maintenance practices aimed at enhancing reliability. In order to ensure the reliability of bearing operation, this article investigates the application of three advanced techniques—Maximum Correlation Kurtosis Deconvolution (MCKD), Multi-Scale Permutation Entropy (MPE), and Long Short-Term Memory (LSTM) recurrent neural networks—for the prediction of the remaining useful life (RUL) of rolling bearings. Each technique's principles, methodologies, and applications are comprehensively reviewed, offering insights into their respective strengths and limitations. Case studies and experimental evaluations are presented to assess their performance in RUL prediction. Findings reveal that MCKD enhances fault signatures, MPE captures complexity, and LSTM excels in modeling temporal patterns. The root mean square error of the prediction results is 0.007. The fusion of these techniques offers a comprehensive approach to RUL prediction, leveraging their unique attributes for more accurate and reliable predictions.

Generalized Bayes is a Bayesian approach based on the learning rate parameter η. In this study, we examine the effect of parameter η on the estimation results considering joint type-I and type-II hybrid censored samples from k exponential populations. In addition to the learning rate parameter, we consider two loss functions, the Linex and general entropy loss functions in the Bayesian approach. Monte Carlo simulations are performed to compare the performances of the estimation results under losses and different values of η. An illustrative example is performed to study the effect of the learning rate parameter and the different losses with different parameters.

Proteins in biological systems function at the interface of single molecule and bulk chemistry and thus provide novel insights into the basic physical chemistry of scaling and emergent phenomena. For example, a binary mechanical model based on the chemistry of muscle contraction unifies molecular mechanics and thermodynamics and provides an explicit solution to the Gibbs paradox. Using the same model system, here I show that chemical activities of molecular states have no effect on chemical kinetics or energetics. Specifically, while the concentration or number of molecules in a molecular state is widely thought to contribute to reaction free energies, here I show that it is not the physical presence of molecules that pushes a reaction forward but the number of microstates, , accessible in a chemical state that pulls a reaction toward equilibrium with an entropic force down an entropic funnel. With the derivation of an entropic contribution to chemical kinetics, I develop a novel chemical kinetic formulation that fully describes the chemical thermodynamics of both equilibrium and non-equilibrium reactions in terms of an a priori system reaction energy landscape.

Intratumor heterogeneity (ITH) is associated with therapeutic resistance and poor prognosis in cancer patients, and attributed to genetic, epigenetic, and microenvironmental factors. We developed a new computational platform, GATHER, for geostatistical modeling of single cell RNA-seq data to synthesize high-resolution and continuous gene expression landscapes of a given tumor sample. Such landscapes allow GATHER to map the enriched regions of pathways of interest in the tumor space and identify genes that have spatial differential expressions at locations representing specific phenotypic contexts using measures based on optimal transport. GATHER provides new applications of spatial entropy measures for quantification and objective characterization of ITH. It includes new tools for insightful visualization of spatial transcriptomic phenomena. We illustrate the capabilities of GATHER using real data from breast cancer tumor to study hallmarks of cancer in the phenotypic contexts defined by cancer associated fibroblasts.

This study aimed to apply different complexity-based methods to surface electromyography (EMG) in order to detect neuromuscular changes after realistic warm-up and stretching procedures. Sixteen volunteers conducted two experimental sessions. They were tested before, after a standardized warm-up, and after a stretching exercise (static or neuromuscular nerve gliding technique). Tests included measurements of the knee flexion torque and EMG of biceps femoris (BF) and semitendinosus (ST) muscles. EMG was analyzed using the root mean square (RMS), sample entropy (SampEn), percentage of recurrence and determinism following a recurrence quantification analysis (%Rec and %Det) and a scaling parameter from a detrended fluctuation analysis. Torque was significantly greater after warm-up as compared to baseline and after stretching. RMS was not affected by the experimental procedure. In contrast, SampEn was significantly greater after warm-up and stretching as compared to baseline values. %Rec was not modified but %Det for BF muscle was significantly greater after stretching as compared to baseline. The a scaling parameter was significantly lower after warm-up as compared to baseline for ST muscle. From the present results, complexity-based methods applied to the EMG give additional information than linear-based methods. They appeared sensitive to detect EMG complexity increases following warm-up.