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.

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.

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.

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.

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 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.

Under the oxidative stress condition, the small RNA (sRNA) Oxys that acts as essential post-transcriptional regulators of gene expression is produced and plays a regulatory function with the assistance of the RNA chaperone Hfq protein. Interestingly, experimental studies found that the N48A mutation of Hfq protein could enhance the binding affinity with OxyS while resulting in defection of gene regulation. But, how the Hfq protein interacts with sRNA Oxys and the origin of the stronger affinity of N48A mutation are both unclear. In this paper, molecular dynamics (MD) simulations were performed on the complex structure of Hfq and OxyS to explore their binding mechanism. The molecular mechanics generalized Born surface area (MM/GBSA) and interaction entropy (IE) method were combined to calculate the binding free energy between Hfq and OxyS sRNA, and the computational result is in excellent correlation with the experimental result. Per-residue decomposition of the binding free energy revealed that the enhanced binding ability of the N48A mutation mainly comes from the increased van der Waals interactions (vdW). This research explores the binding mechanism between Oxys and chaperone protein Hfq, and revealed the origin of the strong binding affinity of N48A mutation. The results provided important insights on the mechanism of gene expression regulation affected by protein mutations.

Pathogen-host interaction (virus-host, bacteria-host and fungi-host) is analyzed from the perspective of biothermodynamics. A mechanistic model of pathogen-host interactions, which was earlier applied to virus-host interactions, was applied for the first time to bacteria-host and fungi-host interactions. Through a mechanistic model suggested in this research, it is possible to explain the phenomenon of tropism of microorganisms to develop infections in certain tissues. Gibbs energy of biosynthesis represents the driving force for growth of bacteria inside host organisms. A growing bacterial colony represents a thermodynamic system, while the host organism is its surroundings. The permissiveness coefficient determines the possibility of growth of bacteria in an appropriate environment (tissue).

Clausius’ virial theorem set a basis for relating kinetic energy in a body of independent material particles to its potential energy, pointing to their complementary role with respect to the second law of maximum entropy. In action mechanics, expressing the entropy of ideal gases as a capacity factor for sensible heat or enthalpy plus the configurational work to sustain the relative translational, rotational and vibrational action yields algorithms for estimating chemical reaction rates and positions of equilibrium. All properties of state including entropy, work potential as Helmholtz and Gibbs energies and activated transition state reaction rates can be estimated, using easily accessible molecular properties, such as atomic weights, bond lengths, moments of inertia and vibrational frequencies. Understanding how Clausius’ virial theorem balances the internal kinetic energy with field potential energy justifies partitioning between thermal and statistical properties of entropy, yielding a more complete view of the evolutionary nature of the second law of thermodynamics. The ease of performing these operations is illustrated by three important chemical gas phase reactions, the reversible dissociation of the hydrogen molecules, lysis of water to hydrogen and oxygen and the reversible formation of ammonia from nitrogen and hydrogen. Employing the ergal also introduced by Clausius to define the reversible internal work to overcome molecular interactions plus the configurational internal work of negative Gibbs energy as a function of volume or pressure may provide a practical guide for managing risk in industrial processes and climate change at the global scale.

SARS-CoV-2 belongs to the group of RNA viruses with a pronounced tendency to mutate. Omicron BA.2.75 is a subvariant believed to be able to suppress the currently dominant BA.5. Omicron BA.2.75 is characterized by a greater infectivity compared to earlier Omicron variants. However, Gibbs energy of biosynthesis of virus particles is slightly less negative compared to those of other variants. Thus, the multiplication rate of Omicron BA.2.75 is lower than that of other variants. This leads to slower accumulation of newly formed virions and less damage to host cells, indicating evolution of SARS-CoV-2 towards decreasing pathogenicity.

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.

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.

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.

One of the intriguing recent results in the field of high-entropy alloys is the discovery of single-phase equiatomic multi-component Laves intermetallics. However, there is no clear understanding that a combination of chemical elements will form such high-entropy compounds. Here we contribute to understanding this issue by modifying the composition of duodenary TiZrHfNbVCrMoMnFeCoNiAl (12x) alloy in which we recently reported the fabrication of hexagonal C14 Laves phase. We consider three alloys based on 12x: 7x=12x-VCrMoMnFe, 12x+Sc, 12x+Be and observe that all of them crystalize with the formation of C14 Laves phase as a dominant structure. We report that 12x+Be alloy reveals single-phase C14 structure with very high concentration of structural defects and ultra-fine dendritic microstructure with almost homogenous distribution of the constituted elements over the alloy matrix. The 7x and 12x+Sc alloys contain C14 as a main phase and unknown impurity phases. To characterize the materials, we examine their heat capacity, electrical conductivity and magnetic properties. The measurements reveal that the Laves phases are Curie-Weiss paramagnets, which demonstrate metallic conduction; 7x and 12x alloys also reveal a pronounced Kondo-like anomaly. Analysis of experimental data as well as ab initio calculations suggests that chemical complexity and compositional disorder cause strong s-d band scattering and thus the rather high density of d-states in the conduction band. Analysis of the results suggests that the mechanism of Laves phase formation in multicomponent multi-principal element metallic alloys is may be the same as in polydisperse hardspheres mixtures. Another important conclusion is that the configurational entropy is a negligible factor in the stabilization of multi-element Laves phases.

Economics has long sought to bridge the principles of microeconomics into the realm of macroeconomics. This paper presents a formal attempt to do so by using a maximum entropy based approach derived from statistical mechanics coupled with subjective game theory and elements from political philosophy. This approach is then applied to income distributions and to the Cobb-Douglas production function, to create a framework for future applications, and to illustrate where past work had made implicit assumptions regarding the system. The paper then explores the consequences of the approach, illustrating self-contradictions in the political philosophy of distributive justice, formally deriving an equation of state for the transactions on the Bitcoin network, and deriving from this the ideal gas law and polytropic process for an economy proving that expansionary monetary policy is not stimulative.

We propose a novel tensor-based formalism for inferring causal structures from time series. An information theoretical analysis of transfer entropy (TE), shows that TE results from transmission of information over a set of communication channels. Tensors are the mathematical equivalents of these multi-channel causal channels. A multi-channel causal channel is a generalization of a discrete memoryless channel (DMC). We consider a DMC as a single-channel causal channel. Investigation of a system comprising three variables shows that in our formalism, bivariate analysis suffices to differentiate between direct and indirect relations. For this to be true, we have to combine the output of multi-channel causal channels with the output of single-channel causal channels. We can understand this result when we consider the role of noise. Subsequent transmission of information over noisy channels can never result in less noisy transmission overall. This implies that a Data Processing Inequality (DPI) exists for transfer entropy.

Information-related measures are useful tools for multi-variable data analysis, as measures of dependence among variables, and as descriptions of order and disorder in biological and physical systems. Measures, like marginal entropies, mutual / interaction / multi -information, have long been used in a number of fields including descriptions of systems complexity and biological data analysis. The mathematical relationships among these measures are therefore of significant inherent interest. Relations between common information measures include the duality relations based on Möbius inversion on lattices. These are the direct consequence of the symmetries of the lattices of the sets of variables (subsets ordered by inclusion). While these relationships are of significant interest there has been, to our knowledge, no systematic examination of the full range of relationships of this diverse range of functions into a unifying formalism as we do here. In this paper we define operators on functions on these lattices based on the Möbius inversions that map functions into one another (Möbius operators). We show that these operators form a simple group isomorphic to the symmetric group S₃. Relations among the set of functions on the lattice are transparently expressed in terms of the operator algebra, and, applied to the information measures, can be used to derive a wide range of relationships among diverse information measures. The Möbius operator algebra is naturally generalized which yields extensive new relationships. This formalism now provides a fundamental unification of information-related measures, and the isomorphism of all distributive lattices with the subset lattice implies an even broader application of these results.

Classification of electromyographic signals has a wide range of applications, from clinical diagnosis of different muscular diseases to biomedical engineering, where their use as input control of prosthetic devices has become a hot topic of research. Challenge of classifying this signals relies on the accuracy of the proposed algorithm and the possibility of its implementation on hardware. This paper consider the problem of electromyography signal classification, solved with the proposed signal processing and feature extraction stages, with focus lying on the signal model and time domain characteristics for better classification accuracy. The proposal considers a simple preprocessing technique that produces signals suitable for feature extraction, and the Burg reflection coefficients to form learning and classification patterns. These coefficients yield a competitive classification rate compared to used time domain features. Sometimes, the feature extraction from electromyographic signals showed that procedure can omit less useful traits for machine learning models. Using feature selection algorithms provides a higher classification performance with as fewer traits as possible. Algorithms achieved a high classification rate up to 100% with low pattern dimensionality, with other kinds of uncorrelated attributes for hand movement identification.

Single valued neutrosophic set has king power to express uncertainty characterized by indeterminacy, inconsistency and incompleteness. Most of the existing single valued neutrosophic cross entropy bears an asymmetrical behavior and produce an undefined phenomenon in some situations. In order to deal with these disadvantages, we propose a new cross entropy measure under single valued neutrosophic set (SVNS) environment namely SN- cross entropy and prove its basic properties. Also we define weighted SN-cross entropy measure and investigate its basic properties. We develop a new multi attribute group decision making (MAGDM) strategy for ranking of the alternatives based on the proposed weighted SN-cross entropy measure between each alternative and the ideal alternative. Finally, a numerical example of MAGDM problem of investment potential is solved to show the validity and efficiency of proposed decision making strategy. We also present comparative anslysis of the obtained result with the results obtained form the existing solution strategies in the solution.

In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. A doping-induced and concentration-dependent phase transition in ZrO₂ under the influence of Y₂O₃ was discovered, due to which the position of the Fermi level changes and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of - 0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The results show that ab initio approaches are able to describe the mechanism of doping-induced phase transitions in (ZrO₂+Y₂O₃)-like systems, based on which it can be assumed that DFT calculations can also flawlessly evaluate other physical and chemical properties of YSZ, which have not yet been studied quantum chemical research. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.

In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. In this case, the position of the Fermi level changes abruptly, and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of - 0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.

The study of the surface thermodynamic properties of solid materials is primordial for the determination of the dispersive surface energy, polar enthalpy of adsorption and Lewis’s acid base properties of solid particles. Inverse gas chromatography technique (IGC) at infinite dilution is the best surface technique for the determination of the surface physicochemical properties of materials. (1) Background: This paper was devoted to study the surface properties of solid materials such as alumina particles by using IGC technique. (2) Methods: Different methods and molecular models such as spherical, cylindrical, van der Waals, Redlich-Kwong, Kiselev and geometric models, were used to determine the London dispersive surface energy of solid surfaces. Hamieh model was also used and highlighted the thermal effect on the surface area of solvents. (3) Results: The variations of the dispersive surface energy and the free energy of adsorption were determined for alumina particles as a function of the temperature as well as their Lewis’s acid base constants. Alumina surfaces were proved to exhibit a strong Lewis amphoteric character three time more basic than acidic (4) Conclusions: The new methodology based on Hamieh model gave the more accurate results of the physicochemical properties of the particle surfaces.

Variability is the predisposition of phenomena to assume different values over time. Variability is higher when the differences of cases from each other are larger or diverge from a specific value, such as arithmetic mean. This study focuses on the variability of research topics within and between research fields to explain, whenever possible, how the variability shapes the structure and dynamics of technological trajectories. Analysis of variability here applies the entropy and variance decomposition on main research fields in quantum technologies. Empirical evidence shows that variability in research topics is inversely proportional to the age of research fields. Inductive implications are that higher variability in research topics of recent scientific fields is due to uncertain dynamics that generates a heterogeneity of different technological trajectories some of them can growth and develop towards fruitful directions others can be dismissed. Hence the variability seems to be one of the drivers that shapes technological evolution and can provide policy and managerial implications to improve the scientific and technological forecasting that may support appropriate decisions of R&D investments towards promising research fields and technologies.

An exposition of entropy applications to highlight some potential entropic applications to artificial intelligence and knowledge transfer. Entropy is a basic idea in artificial intelligence that is applied to many different tasks, such as reinforcement learning, data compression, and decision-making. By quantifying uncertainty and information content, it helps artificial intelligence models provide predictions and decisions that are well-informed. Therefore, this paper shines on spotlighting the significance of entropy to attract the attention of artificial intelligence research community to entropy as a powerful tool to advance artificial intelligence.The significance of knowledge transfer (KT), particularly intergenerational knowledge transfer (IGT), in knowledge management is also covered in this paper. To quantify the complexity of knowledge distribution inside an organisation and assess the efficacy of knowledge transfer (KT) initiatives, the notion of knowledge entropy (KE) is presented. Additionally, the KT model—which is based on the conceptions of tacitness and information content—is introduced. It combines personalisation and codification methodologies. Future research directions are offered alongside a few difficult open problems.

This paper proposes a non-extensive entropy econometric technique to predict energy efficiency at province (NUT-2) level based on imperfect knowledge of the national overall efficiency in the sectors of industry, transport, households and services. The model is applied to the polish case. As acknowledged in recent literature, non-extensive entropy model should remain a valuable device for econometric modelling even in the case of low frequency series since outputs provided by the Gibbs-Shannon entropy approach correspond to the Tsallis entropy limiting case of the Gaussian law when the Tsallis q-parameter converges to unity. Therefore, we set up a q-Tsallis-Kullback-Leibler entropy criterion function with a priori consistency moment and model data constraints, including province energy intensity (known with uncertainty), regional climate differentiation and regular conditions. The model outputs continue to conform to empirical expectations. In spite of the close to unity q-Tsallis parameter, this Tsallis related approach reflects higher stability for parameter computation in comparison with the Shannon-Gibbs entropy econometrics technique. The proposed technique can be applied in different EU countries and elsewhere for example in the context of experimental official statistics.

In this paper, we derive Jeffreys divergence, generalized Fisher divergence and corresponding De Bruijn identities on space-time random field. First, we determine the relation between Fisher information on the space-time random field in one of the space-time points and the ratio of Jeffreys divergence on a space-time random field at distinct space-time positions to the square of coordinate difference. In addition, we also find identities between the partial derivative of the Jeffreys divergence and the generalized Fisher divergence with respect to space-time variables, i.e. the De Bruijn identities, between two space-time random fields obtained by different parameters under the same Fokker-Planck equations. At the end of this paper, we present three examples of the Fokker-Planck equations on space-time random fields, identify their density functions, and derive the Jeffreys divergence, generalized Fisher information, generalized Fisher divergence, and accompanying De Bruijn identities.

The classical Einstein’s Field Equation has been derived previously by demanding that the Clausius relation dS = δQ/T holds. In this letter, we show that the semiclassical Einstein’s Field Equation can be recovered using the generalized entropy Sgen by using the non-equilibrium thermodynamics where the Clausius relation is replaced by the entropy balance relation dS = δQ/T +diS, where diS is some internal entropy. Moreover, since the quantum fields violate the classical focusing, we, therefore, have to use quantum focusing in this case. Using then Jacobson’s idea of thermodynamics of spacetime we recover the semiclassical equation of motion. We, therefore, in a sense also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.

The notion of information and complexity are important concepts in many scientific fields such as molecular biology, evolutionary theory, and exobiology. Many measures of these quantities, either rely on a statistical notion of information, are difficult to compute, or can only be applied to strings. Based on assembly theory, we propose the notion of a \textit{ladderpath}, which describes how an object can be decomposed into a hierarchical structure using repetitive elements. From the ladderpath two measures naturally emerge: the ladderpath-index and the order-index, which represent two axes of complexity. We show how the ladderpath approach can be applied to both strings and spatial patterns and argue that all systems that undergo evolution can be described as ladderpaths. Further, we discuss possible applications to human language and the origins of life. The ladderpath approach provides a novel characterization of the information that is contained in a single object (or a system) and could aid in our understanding of evolving systems and the origin of life in particular.

Clustering algorithms for multi-database mining (MDM) rely on computing $(n^2-n)/2$ pairwise similarities between $n$ multiple databases to generate and evaluate $m\in[1, (n^2-n)/2]$ candidate clusterings in order to select the ideal partitioning which optimizes a predefined goodness measure. However, when these pairwise similarities are distributed around the mean value, the clustering algorithm becomes indecisive when choosing what database pairs are considered eligible to be grouped together. Consequently, a trivial result is produced by putting all the $n$ databases in one cluster or by returning $n$ singleton clusters. To tackle the latter problem, we propose a learning algorithm to reduce the fuzziness in the similarity matrix by minimizing a weighted binary entropy loss function via gradient descent and back-propagation. As a result, the learned model will improve the certainty of the clustering algorithm by correctly identifying the optimal database clusters. Additionally, in contrast to gradient-based clustering algorithms which are sensitive to the choice of the learning rate and require more iterations to converge, we propose a learning-rate-free algorithm to assess the candidate clusterings generated on the fly in a fewer upper-bounded iterations. Through a series of experiments on multiple database samples, we show that our algorithm outperforms the existing clustering algorithms for MDM.

Is it possible to measure the dispersion of ex-ante chances (i.e. chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex-ante chances in various areas with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk to become ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk like the overwhelming majority of the population but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.

In recent years, the individualized demand of customers brings small batches and diversification of orders towards enterprises. The application of enabling technologies in factory, such as the Industrial Internet of Things (IIoT) and Cloud Manufacturing (CMfg), enhances the ability of customer requirement automatic elicitation and the manufacturing process control. The job shop scheduling problem with random job arrival time dramatically increases the difficulty in process management. Thus, how to collaboratively schedule the production and logistics resources in the shop floor is very challenging, and it has a fundamental and practical significance of achieving the competitiveness for an enterprise. To address this issue, the real-time model of production and logistics resources is built firstly. Then, the task entropy model is built based on the task information. Finally, the real-time self-adaption collaboration of production and logistics resources is realized. The proposed algorithm is carried out based on a practical case to evaluate its effectiveness. Experimental results show that our proposed algorithm outperforms three existing algorithms.

Today massive amounts of sequenced metagenomic and -transcriptomic data from different ecological niches and environmental locations are available. Scientific progress depends critically on methods that allow extracting useful information from the various types of sequence data. Here, we will first discuss types of information contained in the various flavours of biological sequence data, and how this information can be interpreted to increase our scientific knowledge and understanding. We argue that a mechanistic understanding is required to consistently interpret experimental observations, and that this understanding is greatly facilitated by the generation and analysis of dynamic mathematical models. We conclude that, in order to construct mathematical models and to test mechanistic hypotheses, time-series data is of critical importance. We review diverse techniques to analyse time-series data and discuss various approaches by which time-series of biological sequence data was successfully used to derive and test mechanistic hypotheses. Analysing the bottlenecks of current strategies in the extraction of knowledge and understanding from data, we conclude that combined experimental and theoretical efforts should be implemented as early as possible during the planning phase of individual experiments and scientific research projects.

The self-assembly is an intriguing process of great importance in general soft matter and thus re-ceives an ever-growing scientific interest. Its most trivial example is the entropy-driven crystalli-zation of hard spheres. Past works have established the similarities and differences in the phase behavior of monomers and chains made of hard spheres. In the present work, inspired by the dif-ference in the melting points of the pure components, we study, through Monte Carlo simulations, the phase behavior of athermal mixtures composed of fully flexible polymers and individual monomers of uniform size. We analyze how the relative number fraction and the packing density affect crystallization and the established ordered morphologies. A synergetic effect is observed in the crystallization leading to synchronous crystallization of the two species. Structural analysis of the resulting ordered morphologies shows perfect mixing and thus no phase separation, which could split the system into polymer-rich and monomer-rich domains. Due to the constraints imposed by chain connectivity, the local environment of the individual spheres is systematically more spherical and more symmetric compared to the one of spheres belonging to chains. In general, increasing polymer content leads to reduction of the degree of crystallinity. According to the present findings, relative concentration is another determining factor to control the phase behavior of hard colloidal systems based on polymers.

To address the issue of traditional static evaluation models being unable to comprehensively analyse the performance of ultra-supercritical coal-fired units under varying loads, we propose a dynamic comprehensive evaluation model based on the improved Criteria Importance Through Inter-criteria Correlation (CRITIC) method and Entropy Weight Method (EWM). The comprehensive performance evaluation index system of ultra-supercritical coal fired units is constructed by examining the boiler performance, turbine performance, plant power performance, environmental performance, and flexible performance of coal powered units. The CRITIC and EWM methods are used to calculate the weights of the indicators, which are then combined with the static evaluation results. Using a dynamic comprehensive evaluation model, we analysed ultra-supercritical coal-fired units, taking into account time weight. This allowed us to obtain the comprehensive dynamic real-time evaluation value of the units under different loads. The research indicates that the dynamic comprehensive evaluation model, which uses an improved CRITIC and EWM, has significant advantages in improving evaluation accuracy, weight-balanced distribution, and generality. Provides more accurate, reasonable, and reliable evaluation results for practical decision making.

Black hole temperature T_BH = T_P/2πd as a function of its Planck length real diameter multiplier d is derived from black hole surface gravity and Hawking temperature w.l.o.g. It is conjectured d = 1/2π describes primordial Big Bang singularity as in this case T_BH = T_P. A black hole interacts with the environment and observable black holes have uniquely defined Delaunay triangulations with a natural number of spherical triangles having Planck areas (bits), where a Planck triangle is active and has gravitational potential of -c² if all its vertices have black hole gravitational potential of -c²/2 and is inactive otherwise. As temporary distribution of active triangles on an event horizon tends to maximize Shannon entropy a black hole is a fundamental, one-sided thermodynamic equilibrium limit for a dissipative structure. Black hole blackbody radiation, informational capacity fluctuations, and quantum statistics are discussed. On the basis of the latter, wavelength bounds for BE, MB, and FD statistics are derived as a function of the diameter multiplier d. It is shown that black holes feature wave-particle duality only if d ≤ 8π, which also sets the maximum diameter of a totally collapsible black hole. This outlines the program for research of other nature phenomena that emit perfect blackbody radiation, such as neutron stars and white dwarfs.

Video capsule endoscopy (VCE) is increasingly used to decrease the discomfort among patients owing to its small size. However, VCE has a major drawback of not having narrow band imaging (NBI) functionality. The current VCE has the traditional white light imaging (WLI) only, which has poor performance in the computer-aided detection (CAD) of different types of cancer compared with NBI. Specific cancers, such as esophageal cancer (EC), do not exhibit any early biomarkers, making their early detection difficult. In most cases, the symptoms are unnoticeable, and EC is diagnosed only in later stages, making its 5-year survival rate below 20% on an average. NBI filters provide particular wavelengths that increase the contrast and enhance certain features of the mucosa, thereby enabling early identification of EC. However, VCE does not have a slot for NBI functionality because its size cannot be increased. Hence, NBI image conversion from WLI can be achieved only in post-processing at present. In this study, a complete arithmetic assessment of the decorrelated color space was conducted to generate NBI images from WLI images for VCE of the esophagus. Three parameters, namely, structural similarity index metric (SSIM), entropy, and peak-signal-to-noise ratio (PSNR), were used to asses the simulated NBI images. Results show the good performance of the NBI image reproduction method, with SSIM, entropy difference, and PSNR values of 93.215%, 4.360, and 28.064 dB, respectively.

Sustainable development of our society demands recycling of metallic wastes which may contain a variety of metallic impurities. Thus, it is desirable to develop a ‘universal’ structure, such as an amorphous alloy tolerating high concentrations of metallic pollutants. We performed ab initio molecular dynamics simulations to manufacture a novel multicomponent amorphous alloy of twenty elements (20e-HEAA). Analysis reveals both topological and chemical compositional short-range ordering in the obtained 20e-HEAA and formation of B-B clusters. Electronic structure calculations reveal the metallic nature of the amorphous alloy with its Fermi level falling in a valley in the density of states. Moreover, the Zn 3d and Cd 4d electrons exhibit a localized nature and thus, should be excluded from the valence electron concentration (VEC) analysis in the study of high-entropy alloys. The information obtained here is helpful to get insight into multicomponent high entropy materials, especially multicomponent high-entropy amorphous alloys as potential circular metals.

Pyrochlore oxides (A2B2O7) are potential nuclear waste substrate material due to their superior radiation resistance properties. We performed molecular dynamics simulations to study the structural properties and displacement cascades in ytterbium titanate pyrochlore (Yb2Ti2O7). We computed threshold displacement energy ( Ed ) and lattice constant ( ao) of Yb2Ti2O7. The effect of displacement cascades in Yb2Ti2O7 of recoils of energies 1 keV, 2 keV, 5 keV, 10 keV in different crystallographic directions ([100], [110], [111]) were studied. The number of defects is found to be proportional to the energy of incident PKA. Additionally, the Ed of pyrochlore is computed and it exhibits anisotropy. Furthermore, radiation damage in high-entropy pyrochlore (HEPy) i.e., YbYTiZrO7, YbGdTiZrO7 , Yb0.5Y0.5Eu0.5Gd0.5TiZrO7 were investigated and compared with Yb2Ti2O7. It was found that HEPy have a larger Ed as compared with Yb2Ti2O7 which exhibits characteristic of lower radiation damage resistance than HEPy. Our simulation proposed that HEPy alloys are more radiation resistant than individual pyrochlore constituents . This work will provide atomic insights in developing substrate materials for nuclear waste applications.

Through a modern derivation of Planck's formula for the entropy of an arbitrary beam of photons we derive a general expression for the entropy production due to the irreversible process of the absorption of an arbitrary incident photon spectrum in material and its dissipation into an infrared-shifted grey-body emitted spectrum, the rest being reflected or transmitted. Employing the framework of Classical Irreversible Thermodynamic theory, we define the generalized thermodynamic flow as the flow of photons from the incident beam into the material and the generalized thermodynamic force is then just the entropy production divided by the photon flow which is the entropy production per unit photon at a given wavelength. We compare the entropy production under sunlight of different inorganic and organic materials (water, desert, leaves and forests) and show that organic materials are the greater entropy producing materials. Intriguingly, plant and phytoplankton pigments (including chlorophyll) have peak absorption exactly where entropy production through photon dissipation is maximal for our solar spectrum $430<\lambda<550$ nm, while photosynthetic efficiency is maximal between 600 and 700 nm. These results suggest that the evolution of pigments, plants and ecosystems has been towards optimizing entropy production rather than photosynthesis. We propose using the wavelength dependence of global entropy production as a biosignature for discovering life on planets of other stars.

In this paper, by extending some results of informational genomics, we present a new randomness test based on the empirical entropy of strings and some properties of repeatability and unrepeatability of substrings of certain lengths. We give the theoretical motivations of our method and some experimental results of its application to a wide class of strings: decimal representations of real numbers, roulette outcomes, logistic maps, linear congruential generators, quantum measurements, natural language texts, and genomes. It will be evident that the evaluation of randomness resulting from our tests does not distinguish among the different sources of randomness (natural, or pseudo-casual).

The objective of the paper is to introduce new similarity measure for single valued neutrosophic sets based on logarithm function. We define logarithm similarity measure and their weighted similarity measure for single valued neutrosophic sets. Then we define hybrid logarithm similarity measure and weighted hybrid logarithm similarity measure for single valued neutrosophic sets. We prove the basic properties of the proposed measures. We then define an entropy function using logarithm function to determine unknown attribute weights. We develop a novel multi attribute group decision making strategy for single valued neutrosophic sets based on the weighted hybrid logarithm similarity measure. We address an illustrative example to demonstrate the effectiveness and aptness of the proposed strategies. We conduct a sensitivity analysis of the developed strategy. We also make a comparison between the obtained results from proposed strategies and different existing strategies in the literature.

Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic hybrid sets to express incomplete information due to the presence of interval valued neutrosophic set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. In this paper we first define a new cross entropy measure under NCSs environment which we call NC- cross entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and applicability, we solve a MADM problem using the proposed strategy.

Telemedicine is the use of Information and Communication Technology (ICT) for clinical health care from a distance. The exchange of radiographic images and electronic patient health information/records (ePHI/R) for diagnostic purposes has the risk of confidentiality, ownership identity, and authenticity. In this paper, a data hiding technique for ePHI/R is proposed. The color information in the cover image is used for key generation, and stego-images are produced with ideal case. As a result, the whole stego-system is perfectly secure. This method includes the features of watermarking and steganography techniques. The method is applied to radiographic images. For the radiographic images, this method resembles watermarking, which is an ePHI/R data system. Experiments show promising results for the application of this method to radiographic images in ePHI/R for both transmission and storage purpose.

The rapid convergence of Artificial General Intelligence (AGI), autonomous drones, and applied robotics presents a transformative opportunity for many sectors. However, this advancement also raises critical ethical and existential questions, particularly in warfare. This paper explores the concept of entropy as a metaphor for the potential disorder introduced by these increasingly complex technologies. We examine the risks of AGI surpassing human control in conflict situations, where autonomous decision-making could have disastrous consequences. We then analyze autonomous drones, scrutinizing their impact on warfare tactics and the ethical dilemmas surrounding independent, real-time decision-making. Finally, we investigate applied robotics in military operations, focusing on the delicate balance between enhanced capabilities and the potential for uncontrollable systems. Through a multidisciplinary lens, drawing on technology ethics, military strategy, and AI safety, this paper utilizes the concept of entropy to highlight the need for caution in developing these technologies. We propose a scientifically grounded and ethically sound framework to guide policymakers, technologists, and ethicists in navigating the path between innovation and global stability. This framework concludes with recommendations for responsible development and deployment strategies that can mitigate the risks associated with these powerful tools.

In this work we identify combinations of technological activities that signal the presence local capabilities in a country to successfully export a product. We use country-level patent and trade data to generate a multi-layer network, and we apply maximization of entropy to generate synthetic data to effectively divide signal from noise. We show that in several sectors the signal far exceed the noise. Our exercise provides robust evidence of the presence of synergies between technologies to explain trade performances in specific markets. This can be highly useful for policy makers, to inform industrial and innovation policies.

This paper constitutes an original and new methodology for the determination of the surface properties of carbon fibers in the two oxidized and untreated forms by inverse gas chromatography technique at infinite dilution based on the effect of the temperature on the surface area of the various organic molecules adsorbed on the carbon fibers. The studied thermal effect proved a large deviation of the classical methods or models relative to the new determination of the surface properties of carbon fibers, such as the dispersive component of their surface energy, the free surface energy, the free specific energy, the enthalpy and entropy of adsorption of molecules on the carbon fibers. The obtained specific enthalpy and entropy of adsorption for the polar solvents led to the determination of the Lewis’s acid-base constants of carbon fibers. Different molecular models and chromatographic methods were used to quantify the surface thermodynamic properties of carbon fibers and compared to the thermal model. The obtained results proved that the oxidized carbon fibers gave more specific interaction energy and greater acid-base constants than that of the untreated carbon fibers and thus highlighting the important role of the oxidization on the acid-base of fibers. The determination of the specific acid-base surface energy of the two carbon fibers showed greater values of the oxidized carbon fibers relative to the untreated carbon fibers. An important basic character was highlighted for the two studied carbon fibers, larger than the acidic character. It was observed that the Lewis’s acid-base constants of the oxidized carbon fibers are larger than that of the untreated fibers with more accentuated basic charterer. This result was confirmed by all molecular models and chromatographic methods.

The theory of Ismail's non-extensive maximum entropy solution (NME) is described in detail. It is used as an inductive inference technique for heavy-tailed queues with a non-robust mean queue length and a non-extensive "long-range" interaction. In our novel method, we substitute the non-robust mean queue length for the conventional Pollaczeck-Khinchin mean queue length. In other words, the new non-extensivity parameter q will be included in the resulting state probability function. Numerical portraits are provided to capture the influential effect of the derived formalism, , on the stable M//1 queue with heavy tails. More potentially, some applications of Hurst Exponent to social computing and connected health are provided. Conclusion with some challenging open problems and possible future research pathways are given.

In this study, we considered the structural stability, electronic properties, and phonon dispersion of the cubic (c-ZrO₂), tetragonal (t-ZrO₂), and monoclinic (m-ZrO₂) phases of ZrO₂. We found that the monoclinic phase of zirconium dioxide is the most stable among the three phases in terms of total energy, lowest enthalpy, highest entropy, and other thermodynamic properties. The smallest negative modes were found for m-ZrO₂. Our analysis of the electronic properties showed that during the m–t phase transformation of ZrO₂, the Fermi level first shifts by 0.125 eV toward higher energies and then decreases by 0.08 eV in the t–c cross-section. The band gaps for c-ZrO₂, t-ZrO₂, and m-ZrO₂ are 5.140 eV, 5.898 eV, and 5.288 eV, respectively. Calculations based on the analysis of the influence of doping 3.23, 6.67, 10.35, and 16.15 mol. %Y₂O₃ onto the m-ZrO₂ structure showed that the enthalpy of m-YSZ decreases linearly, which accompanies further stabilization of monoclinic ZrO₂ and an increase in its defectiveness. The doping-induced and concentration-dependent phase transition of zirconium dioxide under the influence of yttrium oxide was studied, after which the position of the Fermi level changes and the energy gap decreases. It has been established that, not only for pure systems but including those doped with Y₂O₃, the main contribution to the formation of the conduction band is made by the p-states of electrons. The t-ZrO₂ (101) and t-YSZ (101) surface models were selected as optimal surfaces for water adsorption based on a comparison of their surface energies. An analysis of the mechanism of water adsorption on the surface of t-ZrO₂ (101) and t-YSZ (101) showed that H₂O on unstabilized t-ZrO₂ (101) is adsorbed dissociatively with an energy of -1.22 eV, as well as by the method of molecular chemisorption with an energy of -0.69 eV and the formation of a hydrogen bond with a bond length of 1.01 Å. In the case of t-YSZ (101), water is molecularly adsorbed onto the surface with an energy of -1.84 eV. Dissociative adsorption of water occurs at an energy of -1.23 eV, near the yttrium atom. The calculations showed that ab initio research methods are capable of describing the mechanism of phase transitions of materials under the influence of alloying. That is, by optimizing the parameters of DFT calculations, it is possible to observe the effects of doping on other physical and chemical properties of materials, which are still beyond the scope of quantum chemical modeling. The obtained results complement the database of research works carried out in the field of the application of biocompatible zirconium dioxide crystals and ceramics in green energy generation and can be used in designing humidity-to-electricity converters and creating solid oxide fuel cells based on ZrO₂.

We have now identified two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type A energy processes such as the classical heat engines, apparently well follow the second law of thermodynamics; Type B energy processes, such as the newly discovered thermotrophic function that isothermally utilizes environmental heat energy to do useful work in driving ATP synthesis, which follows the first law of thermodynamics (conservation of mass and energy) but does not have to be constrained by the second law, owing to their special asymmetric functions. Several Type-B energy processes such as asymmetric-function-gated isothermal electricity and epicatalysis have been created through human efforts. The innovative efforts on Type-B processes to enable isothermally utilizing endless environmental heat energy could help to liberate all peoples from their dependence on fossil fuel energy, thus helping to reduce greenhouse gas CO2 emissions and control climate change towards a sustainable future for the humanity on Earth.

Brain-Computer Interface (BCI) systems can assist physically challenged people to interact with their surroundings and improve the quality of their lives. Decoding human thoughts is a powerful technique that can assist paralyzed people who have lost their speech production ability. Speaking is a combined process involving synchronizing the brain and the oral articulators. This paper proposed a high-accuracy brain wave pattern recognition based on inner speech using a novel feature extraction method. Only eight EEG electrodes were used in this study, and they were set on selected spots on the scalp. Support Vector Machine (SVM) was employed to decode the recorded EEG dataset into four internally spoken words which are: Up, Down, Left, and Right. The proposed approach achieved overall classification accuracy that ranges between 96.20% to 97.5%. In addition, more performance evaluation metrics were estimated to test the reliability of classifying the EEG-based inner speech data, and we obtained 97.61%, 97.50%, and 97.73% for F1-score, recall, and precision respectively. Furthermore, the Area Under Curve of the Receiver Operating Characteristic (AUC-ROC) proved the strength of the proposed approach for classifying the specified inner speech commands by achieving a macro-average amount of 99.32%. The inner speech classification method using electroencephalography proposed in this work can clinically help improve communication for patients with problems including speech disorder, mutism, cognitive development, executive function, and psychopathology.

Hand gestures are an essential part of human-to-human communication and interaction, and therefore for technical applications, the aim is increasingly to achieve interaction between humans and computers that is as natural as possible, for example by means of natural language or hand gestures. In the context of human-machine interaction research, these methods are consequently being explored more and more. However, the realization of natural communication between humans and computers is a major challenge. In the field of hand gesture recognition, research approaches are being pursued that use additional hardware such as special gloves to classify gestures with high accuracy. Recently, deep learning techniques using artificial neural networks have been increasingly proposed for the problem of gesture recognition without using such tools. In this context, in our approach convolutional neural network (CNN) will be explored in detail for the task of hand gesture recognition. CNN is a deep neural network that can be used in the field of visual object processing and classification. The goal of this work is to recognize ten types of static hand gestures in front of complex backgrounds and different hand sizes based on raw images without the use of extra hardware. We achieved good results with a CNN network architecture consisting of seven layers. Through data augmentation and skin segmentation, a significant increase of the model accuracy was achieved. On public benchmarks the ten gestures have been classified almost perfectly with a testing accuracy of 96.5%

The service conditions of underground coal mine equipment are poor, and it is difficult to accurately extract the fault characteristics of rolling bearings. In order to better improve the accuracy of fault identification of rolling bearings, a fault detection method based on multiscale permutation entropy and SOA-SVM is proposed. First, the whale optimization algorithm is used to select the modal analysis number K and the penalty factor α of the variational mode decomposition algorithm. Then, the vibration signal of rolling bearings is dissolved according to the optimized variational mode decomposition algorithm, and the multi-scale permutation entropy of the main intrinsic mode function is calculated. Finally, the feature values of the matrix are entered into the SVM algorithm optimized by the seagull optimization algorithm to obtain the classification result. The experimental results based on the published rolling bearing datasets of Western Reserve University show that the identification success rate of the proposed method can reach 98.75%. The fault detection of the rolling bearings can be completed accurately and efficiently.

The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of scienThe Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.ce, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.

My innovative entropy measure, Ismail entropy, namely, (IE) is an ultimate generalization to numerous generalized entropies within the literature. The fractal dimension of IE is identified in this paper. On another applicative note, this paper offers some potential applications of fractal dimension to smart cities. The paper ends with closing remarks combined with some challenging open problems and the next phase of research.

The temporo-spatial theory of consciousness postulates that the brain implements its own inner time and space for conscious processing of outside world. In line with this hypothesis, I present a mechanistic model of mutually connected processes that encode the inner space and time. The model is used to elaborate the binding mechanism between two sets of processes representing the inner space and time, respectively. Further, a stochastic version of the model is developed to investigate the interplay between the binding strength and noise. The spectral entropy is used to characterize the noise effects on the systems of processes when the binding strength is varied. The stochastic modeling results reveal that the spectral entropy values for strongly bound systems have similar entropy values for weakly bound or even decoupled systems. Thus, the analysis performed in this study allows to conclude that the binding mechanism is noise-resilient.

We present results on the spontaneous crystallization of freely-jointed polymers of hard spheres obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous configuration and after a transitory dominance of the hexagonal closed packed (HCP) polymorph, the system crystallizes in a final, stable, face centered cubic (FCC) crystal of very high perfection. Through refined metrics we gauge the degree of ordering and identify the regions of the phase transition and the corresponding morphologies. An analysis of chain conformational characteristics, of the spatial distribution of monomers and of the volume accessible to them shows that the phase transition is caused by an increase in translational entropy that is larger than the loss of conformational entropy of the chains in the crystal compared to the amorphous state. Polymer chains in the crystal adopt ideal random walk statistics as their great length renders local conformational details, imposed by the geometry of the FCC crystal, irrelevant.

Computationally modelling a nuclear reactor startup core for a benchmark against the existing models is highly desirable for an independent assessment informing nuclear engineers and energy policymakers. This work presents a startup core model of the UK’s first Evolutionary Pressurised Water Reactor (EPR) based on Monte Carlo simulations of particle collisions using Serpent 2, a continuous-energy Monte Carlo reactor physics burnup code. Coupling between neutronics and thermal-hydraulic conditions with the fuel depletion is incorporated into the multi-dimensional branches, obtaining the thermal flux and fission rate (power) distributions radially and axially from the three dimensional (3D) single assembly level to a 3D full core. Shannon entropy is employed to characterise the convergence of the fission source distribution, with 3 billion neutron histories tracked by parallel computing. Source biasing is applied for the variance reduction. Benchmarking the proposed Monte Carlo 3D full-core model against the traditional deterministic transport computation suite used by the UK Office for Nuclear Regulation (ONR), a reasonably good agreement within statistics is demonstrated for the safety-related reactivity coefficients, which creates trust in the EPR safety report.

Natural time is a new time domain introduced in 2001. The analysis of time series associated with a complex system in natural time may provide useful information and may reveal properties that are usually hidden when studying the system in conventional time. In this new time domain, an entropy has been defined and complexity measures based on this entropy as well as its value under time-reversal have been introduced and found applications in various complex systems. Here, we review these applications in the electric signals that precede rupture, e.g., earthquakes, in the analysis of electrocardiograms, as well as in global atmospheric phenomena like the El Nino/La Nina Southern Oscillation.

Ontological premises have profound theoretical implications. This analysis posits a single, universal structure composed of two ontic entities: discrete, quantized units of space ("Planck Spheres") and a State of Absolute Nothingness (the "SOAN"). Planck Spheres and the SOAN form a physical, ultra-high (3 x N) dimensional space ("Planck Space") and a discrete 3D space (or "4D spacetime"). Together, Planck Space and 4D spacetime form a tightly integrated ((3 x N) + 3) hyperspace (the "Dual Ontology"). Critically, a one-to-one mapping and identity exists between the Planck Spheres comprising 4D spacetime and Planck Space. The Dual Ontology conjecture supports radically simplified physical explanations for three distinct areas of theoretical physics: First, the conjecture reconciles fundamental issues in Special Relativity and quantum mechanics by explaining why single and N-body quantum states (a) dynamically evolve in 4D spacetime subject to the speed of light and (b) instantaneously collapse in a physical Planck Space that is not subject to Special Relativity. Second, the temporal and physical asymmetry between the dynamic evolution of quantum states in 4D spacetime subject to Special Relativity and the instantaneous collapse of quantum states in a Planck Space where Special Relativity is inapplicable explains quantum path irreversibility and the arrow of time. Third, at or near the heat death of 4D spacetime, the instantaneous collapse of the energy content of Planck Space and the simultaneous transition of 4D spacetime's extremely widely dispersed energy content to a non-singular, generally localized volume at t = 0 explains 4D spacetime's isotropy, homogeneity, extremely high energy, pressure, and temperature, flatness, and low gravitational entropy. It also explains the horizon and fine-tuning problems.

There are currently around 78 Nuclear Power Plants (NPP) in the world based on Boiling Water Reactors (BWR). The current parameter to assess BWR instability issues is the linear Decay Ratio (DR). However, it is well known that BWRs are complex non-linear dynamical systems that may even exhibit chaotic dynamics that normally preclude the use of the DR when the BWR is working at a specific operating point during instability. In this work a novel methodology based on an adaptive Shannon Entropy estimator and on Noise Assisted Empirical Mode Decomposition variants is presented. This methodology was developed for real-time implementation of a stability monitor. This methodology was applied to a set of signals stemming from several NPPs reactors (Ringhals-Sweden, Forsmark-Sweden and Laguna Verde-Mexico) under commercial operating conditions, that experienced instabilities events, each one of a different nature

The spatial resolution measurement limitation of the position-momentum uncertainty principle is shown to mathematically originate from the Bekenstein entropy bound and the associated second law of thermodynamics, as a special case in which a statistical thermodynamic distribution of energies is specialized to a fixed, definite probe energy equal to the average energy of that distribution. This is used in combination with the Wein displacement law to predict an ultraviolet cutoff for Planck blackbody radiation at about ⅛ of the Wein peak. A new UV photon counting experiment is proposed to test for this. A physical understanding of these results may be provided by a UV-complete, intelligible theory of general relativistic quantum mechanics in which the observation of a blackbody spectrum is simply a remote observation of Hawking radiation emitted from black hole fluctuations in the gravitational vacuum.

According to the current European and Italian scenario related to urban re-generation, cultural and landscape heritage, valorisation is being also enhanced by the activation of innovative processes. These involve the development of methodologies and tools that are able to address decision-making processes among low entropy economy, complex values and creative practices. In this perspective, the research aims to investigate the possibilities of developing a Cultural Heritage Low Entropy Enhancement (CHLEE) approach by considering how the complex values of cultural heritage can vary not only through a physical transformation of spaces but also through a program of uses and activities able to produce new values, where the human experience is essential. This type of model modifies the objectives that characterise the valorisation of cultural heritage and landscape, recognising that the fruition is no longer “consumerist” but “experiential”. A crucial role is represented by the heterogeneity of creative practices that contribute to the identificationidentifying and implementation ofimplementing innovative management and governance models. The present paper explores the components of creative regenerative processes, based upon the ex-post evaluation of some Italian experiments, across the PROMETHEE-GAIA multi-criteria method, to understand how creative experiences are building innovation ecosystem thanks to low entropy economy and improve the ex-ante evaluation for new strategies and policies.

Primary energy consumption is one of the key drivers of global CO₂ emissions that, in turn, heavily depend on the efficiency of involved technologies. Either the improvement in technology efficiency or the expansion of non-fossil fuel consumption require large investments. The planning and financing of such investments, by policy makers or global energy firms, require, in turn, reliable measures of associated global spreads and their evolution in time. In this paper, our main contribution is the introduction of index measures for accessing global spreads (that is, measures of inequality or inhomogeneity in the statistical distribution of a related quantity of interest) of technology efficiency and CO₂ emission in primary energy consumption. These indexes are based on the Gini index, as used in economical sciences, and generalised entropy measures. Regarding primary energy sources, we consider petroleum, coal, natural gas and non-fossil fuels. Between our findings, we attest some stable relations in the evolution of global spreads of technology efficiency and CO₂ emission, and a positive relation between changes in global spreads of technology efficiency and use of non-fossil fuel.

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

Here we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is based on two primary postulates: that small systems can be treated self-consistently by coupling them to an ensemble of similarly small systems, and that a large ensemble of small systems forms its own thermodynamic bath. We adapt this “nanothermodynamics” to investigate how a large system may subdivide into an ensemble of smaller subsystems, causing internal heterogeneity across multiple size scales. For the semi-classical ideal gas, maximum entropy favors subdividing a large system of “atoms” into an ensemble of “regions” of variable size. The mechanism of region formation could come from quantum exchange symmetry that makes atoms in each region indistinguishable, while decoherence between regions allows atoms in separate regions to be distinguishable by their distinct locations. Combining regions reduces the total entropy, as expected when distinguishable particles become indistinguishable, and as required by a theorem in quantum mechanics for sub-additive entropy. Combining large volumes of small regions gives the usual entropy of mixing for a semi-classical ideal gas, resolving Gibbs paradox without invoking quantum symmetry for atoms that may be meters apart. Other models presented here are based on Ising-like spins, which are solved analytically in one dimension. Focusing on the bonds between the Ising-like spins we find similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for fully-accurate predictions. Another result using Ising-like spins involves simulations that include a nonlinear correction to Boltzmann’s factor, which mimics the statistics of indistinguishable states by imitating the dynamics of spin exchange on intermediate lengths. These simulations exhibit 1/f-like noise at low frequencies (f), and white noise at higher f, similar to equilibrium thermal fluctuations found in many materials.

A simple line of reasoning, based on the most fundamental concepts of thermodynamics, yields some intriguing results for a better understanding of the processes occurring in the observable Universe. Gravitational mass must be continuously generated within an expanding thermodynamic system for this system to remain closed. The Second Law is a direct consequence of this production of mass. Simple expressions for the entropy and temperature of the Universe were obtained and the results agree well with observable values. Furthermore, it is demonstrated that the conservation laws within the Universe are independent of its energy density. Based on the solution for the quantum state of the Universe, it is conjectured that the Second Law is incomplete and must be complemented to a conservation law, which takes into account the growth of the amount of information within the Universe. Once the Second Law is complemented to a conservation law, the importance of mass generation within the Universe becomes well pronounced – not only gravitational effects play the role of an organising force, but also the amount of mass within the Universe defines both the amount of information within the Universe and the level of the Universe’s complexity.

The article obtains large deviation asymptotic for sub-critical communication networks modelled as signal-interference-noise-ratio(SINR) random networks. To achieve this, we define the empirical power measure and the empirical connectivity measure, as well as prove joint large deviation principles(LDPs) for the two empirical measures on two different scales. Using the joint LDPs, we prove an Asymptotic equipartition property(AEP) for wireless telecommunication Networks modelled as the subcritical SINR random networks. Further, we prove a Local Large deviation principle(LLDP) for the sub-critical SINR random network. From the LLDPs, we prove the large deviation principle, and a classical McMillan Theorem for the stochastic SINR model processes. Note that, the LDPs for the empirical measures of this stochastic SINR random network model were derived on spaces of measures equipped with the $\tau-$ topology, and the LLDPs were deduced in the space of SINR model process without any topological limitations. We motivate the study by describing a possible anomaly detection test for SINR random networks.

The determination of the specific surface free energy, specific properties and Lewis’s acid base of solid materials is of capital importance in many industrial processes such as adhesion, coatings, two dimensional films and adsorption phenomena. (1) Background: The physicochemical properties of many solid particles were characterized during the last forty years by using the retention time of injected well-known molecules into chromatographic column containing the solid substrates to be characterized. The obtained net retention time of the solvents adsorbed on the solid allowing the determination of the net retention volume directly correlated to the specific surface variables, dispersive, polar and acid-base properties. (2) Methods: Many chromatographic methods were used to quantify the values of the different specific surface variables of the solids. However, one found a large deviation between the different results. In this paper, one proposed a new method that quantify the specific free energy of adsorption as well as the Lewis’s acid-base constants of many solid surfaces. (3) Results: The new applied method allowed us to obtain the specific enthalpy and entropy of adsorption of polar model organic molecules on several solid substrates such as silica, alumina, MgO, ZnO, Zn, TiO2 and carbon fibers. (4) Conclusions: our new method based on the separation between the dispersive and polar free surface energy allowed to better characterize the solid materials.

Research for a theory of quantum gravity has recently led to the use of presheaf topos. Quantum uncertainty is linked to the truth values of intuitionistic logic. This paper proposes transposing this model into a classic probability context, that of conditional mathematical expectations. A simulation of Brownian motion is offered for illustrative purposes.

In this paper, the problem of predicting future failure times based on a jointly type-II censored sample from k exponential populations is considered. The Bayesian prediction intervals and point predictors were then obtained. Generalized Bayes is a Bayesian study based on a learning-rate parameter. This study investigated the effects of the learning rate parameters on the prediction results. The loss functions of squared error, Linex, and general entropy were used as point predictors. Monte Carlo simulations were performed to show the effectiveness of the learning rate parameter in improving the results of prediction intervals and point predictors.

One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D Cluster Variation Method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy and the interaction enthalpy. Initial investigations with two different representative topographies (``scale-free-like'' and ``rich club-like'') produce interesting results when brought to a CVM free energy minimum. Additional phase space investigations, where one of these two parameters has been set to zero, identify useful parameter ranges. Careful comparison of the analytically-predicted configuration variables versus those obtained when performing computational free energy minimization on a 2-D grid show that the computational results differ significantly from the analytic solution. The 2-D CVM can potentially function as a secondary free energy minimization within the hidden layer of a neural network, providing a basis for extending node activations over time and allowing temporal correlation of patterns.

This paper describes a proposed fractional filter-based multi-scale underwater and hazy image enhancement algorithm. The proposed system combines a modified global contrast operator with fractional order-based multi-scale filters used to generate several images, which are fused based on entropy and standard deviation. The multi-scale-global enhancement technique enables fully adaptive and controlled colour correction and contrast enhancement without over exposure of highlights when processing hazy and underwater images. This in addition to illumination/reflectance estimation coupled with global and local contrast enhancement. The proposed algorithm is also compared with the most recent available state-of-the-art multi-scale fusion de-hazing algorithm. Experimental comparisons indicate that the proposed approach yields better edge and contrast enhancement results without halo effect, colour degradation and is faster and more adaptive than all other algorithms from the literature.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

In this paper we describe and exploit a geometric framework for Gibbs probability densities and the associated concepts in statistical mechanics, which unifies several earlier works on the subject, including Souriau's symplectic model of statistical mechanics, its polysymplectic extension, Koszul model, and approaches developed in quantum information geometry. We emphasize the role of equivariance with respect to Lie group actions and the role of several concepts from geometric mechanics, such as momentum maps, Casimir functions, coadjoint orbits, and Lie-Poisson brackets with cocycles, as unifying structures appearing in various applications of this framework to information geometry and machine learning. For instance, we discuss the expression of the Fisher metric in presence of equivariance and we exploit the property of the entropy of the Souriau model as a Casimir function to apply a geometric model for energy preserving entropy production. We illustrate this framework with several examples including multivariate Gaussian probability densities, and the Bogoliubov-Kubo-Mori metric as a quantum version of the Fisher metric for quantum information on coadjoint orbits. We exploit this geometric setting and Lie group equivariance to present symplectic and multisymplectic variational Lie group integration schemes for some of the equations associated to Souriau symplectic and polysymplectic models, such as the Lie-Poisson equation with cocycle.

Managing sidelobe levels (SLLs) in metasurface-driven beam-steering antennas poses a significant challenge due to intrinsic factors leading to grating lobes. Our proposed method employs an equivalent model to optimize large periodic metasurfaces efficiently. This model predicts complete metasurface performance, accounting for mutual coupling between patches. We introduce an evolutionary optimization algorithm based on the Cross Entropy (CE) method to enhance PGM-based beam-steering antennas and suppress sidelobes. Two strategies were employed: first is to optimize the patch dimensions for a sidelobe-free pattern and the second is to maintain the PGM dimensions while optimizing feed array amplitudes. Both strategies effectively suppressed sidelobes, offering insights into the CE method's applicability and effectiveness for CPU-intensive electromagnetic optimization challenges. The proposed CE method variant retains its simplicity while improving monitoring capabilities, addressing this limitation. Smaller generations yield better improvements per evaluation

Mereology stands for the philosophical concept of parthood and is based on a sound set of fundamental axioms and relations. One of these axioms relates to the existence of a universe as a thing having part all other things. The present article formulates this logical expression first as an algebraic inequality and eventually as an algebraic equation reading in words: The universe equals the sum of all things. “All things” here are quantified by a “number of things”. Eventually this algebraic equation is normalized leading to an expression The whole equals the sum of all fractions. This introduces “1” or “100%” as a quantitative – numerical - value describing the “whole”. The resulting “basic equation” can then be subjected to a number of algebraic operations. Especially squaring this equation leads to correlation terms between the things implying that the whole is more than just the sum of its parts. Multiplying the basic equation (or its square) by a scalar allows for the derivation of physics equations like the entropy equation, the ideal gas equation, an equation for the Lorentz-Factor, conservation laws for mass and energy, the energy-mass equivalence, the Boltzmann statistics, and the energy levels in a Hydrogen atom. It further allows deriving a “contrast equation” which may form the basis for the definition of a length and a time scale. Multiplying the basic equation with vectors, pseudovectors, pseudoscalars and eventually hypercomplex numbers opens up the realm of possibilities to generate many further equations.

In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their "space of evolution" associated to a homogeneous symplectic manifold by a Lagrange 2-form, and defines in case of non null cohomology (non equivariance of the coadjoint action on the moment map with appearance of an additional cocyle) a Gibbs density (of maximum entropy) that is covariant under the action of dynamic groups of physics (eg, Galileo's group in classical physics). Souriau Lie Group Thermodynamics was also addressed 30 years after Souriau by R. F. Streater in the framework of Quantum Physics by Information Geometry for some Lie algebras, but only in the case of null cohomology. Souriau method could then be applied on Lie Groups to define a covariant maximum entropy density by Kirillov representation theory. We will illustrate this method for homogeneous Siegel domains and more especially for Poincaré unit disk by considering SU(1,1) group coadjoint orbit and by using its Souriau’s moment map. For this case, the coadjoint action on moment map is equivariant. For non-null cohomology, we give the case of Lie group SE(2). Finally, we will propose a new geometric definition of Entropy that could be built as a generalized Casimir invariant function in coadjoint representation, and Massieu characteristic function, dual of Entropy by Legendre transform, as a generalized Casimir invariant function in adjoint representation, where Souriau cocycle is a measure of the lack of equivariance of the moment mapping.

In the present work we revise and extend the Characteristic Crystallographic Element (CCE) norm, an algorithm used to simultaneously detect radial and orientational similarity of computer-generated structures with respect to specific reference crystals and local symmetries. Based on the identification of point group symmetry elements, the CCE descriptor is able to gauge local structure with high precision and finely distinguish between competing morphologies. As test cases we use computer-generated monomeric and polymer systems of spherical particles interacting with the hard-sphere and square-well attractive potentials. We demonstrate that the CCE norm is able to detect and differentiate, between others, among: hexagonal close packed (HCP), face centered cubic (FCC), hexagonal (HEX) and body centered cubic (BCC) crystals as well as non-crystallographic fivefold (FIV) local symmetry in bulk 3-D systems; triangular (TRI), square (SQU) and honeycomb (HON) crystals, as well as pentagonal (PEN) local symmetry in thin films of one-layer thickness (2-D systems). The descriptor is general and can be applied to identify the symmetry elements of any point group for arbitrary atomic or particulate system in two or three dimensions, in the bulk or under confinement.

Information geometry (IG) seeks to characterize the structure of statistical geodesic models from a differential geometric point of view. By considering families of probability distributions as manifolds with coordinate charts determined by the parameters of each individual model, the tools of differential geometry, such as divergences and metric tensors, provide effective means of studying their characteristics. The research undertaken in this paper presents a novel approach to the modelling study of information geometrics of a queueing system. In this context, the manifold of a stable M/G/1queue is characterised from the viewpoint of IG. The Fisher Information matrix (FIM) as well as the inverse of (FIM), (IFIM) of stable M/G/1 queue manifold are devised. In addition to that, new results that uncovered the significant impact of stability of M/G/1 queue manifold on the existence of (IFIM) are obtained. The Kullback’s divergence (KD), and J-divergence (JD).New result has been devised on the significant impact of both server utilization and squared coefficient of variation of the underlying M/G/1 queue manifold on both (KD) and (KD) are devised. Also, it is revealed that stable M/G/1 QM is developable (i.e., has a zero Gaussian curvature) and has a non-zero Ricci Curvature Tensor (RCT). Novel stability dynamics of M/G/1 queue manifold is revealed by discovering the mutual dual impact between the behaviour of (RCT) and the stability and the instability phases of the underlying M/G/1 queue manifold. Furthermore, a new discovery that presents the significant impact of stability of M/G/1 queue manifold and the continuity of the unique representation between M/G/1 queue manifold and Ricci Curvature Tensor (RCT). The information matrix exponential (IME) is devised. It is also shown that the obtained (IME) is unstable. Also, it is shown that stability of the devised (IME) enforces the instability of M/G/1 queue manifold. Unifying IG with Queueing Theory enables the study of dynamics of queueing system from a novel Riemannian Geometric (RG) point of view, leading to the analysis of the stable M/G/1 queue, based on the Theory of Relativity (TR).Extending the study over two new additional divergence measures, namely and together with a complete illustrative numerical results for all these measures including KD, JD. This links Queueing theory, IG with deep machine learning and metric learning. Furthermore, this reveals the revolutionary approach of queue learning. Full analytic study of Gaussian curvatures subject to both Angular and Monge techniques together with the overall stability dynamics impact on these curvatures. Full analytic study of Einestein Tensor and Stress Energy Tensor together with the overall stability dynamics impact on these curvatures. The inclusion of the definitions of Gaussian and Ricci, Ricci scalar curvatures and Einstein Tensor together with their physical interpretations; The proposed novel approach for the pioneer visualization of queueing systems via computational information geometry. The determination of new important links between classical queueing theory and other mathematical disciplines, such as IG, matrix theory Riemannian geometry and the THEORY OF RELATIVITY by providing for first time i) The full detailed derivations of the Gaussian curvature ii) The Ricci curvature tensor and iii) The full physical as well as the geometric interpretation of these new results. The provision of a novel link between Ricci Curvature (RCT) and the stability analysis of the stable M/G/1 QM. The full investigation of the newly introduced QT-IG unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them. The full investigation of the newly introduced (QIGU) unifiers together with the impact of stability/ instability of the underlying M/G/1 QM on them.