Version 1
: Received: 7 September 2024 / Approved: 8 September 2024 / Online: 9 September 2024 (08:43:17 CEST)
How to cite:
Ataei, M.; Wang, X. Derangetropy in Probability Distributions and Information Dynamics. Preprints2024, 2024090611. https://doi.org/10.20944/preprints202409.0611.v1
Ataei, M.; Wang, X. Derangetropy in Probability Distributions and Information Dynamics. Preprints 2024, 2024090611. https://doi.org/10.20944/preprints202409.0611.v1
Ataei, M.; Wang, X. Derangetropy in Probability Distributions and Information Dynamics. Preprints2024, 2024090611. https://doi.org/10.20944/preprints202409.0611.v1
APA Style
Ataei, M., & Wang, X. (2024). Derangetropy in Probability Distributions and Information Dynamics. Preprints. https://doi.org/10.20944/preprints202409.0611.v1
Chicago/Turabian Style
Ataei, M. and Xiaogang Wang. 2024 "Derangetropy in Probability Distributions and Information Dynamics" Preprints. https://doi.org/10.20944/preprints202409.0611.v1
Abstract
We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides deeper insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory.
Keywords
Information Dynamics; Probability Distributions; Functional Measures; Entropy; Combinatorial Analysis; Differential Equations; Information Theory; Equilibrium Analysis
Subject
Computer Science and Mathematics, Artificial Intelligence and Machine Learning
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
