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Derangetropy in Probability Distributions and Information Dynamics.

Masoud Ataei1, Xiaogang Wang2

  • 1Department of Mathematical and Computational Sciences, University of Toronto, Mississauga, ON L5L 1C6, Canada.

Entropy (Basel, Switzerland)
|November 27, 2024
PubMed
Summary
This summary is machine-generated.

We introduce derangetropy, a new measure for information dynamics in probability distributions. This functional approach captures information dispersion, offering insights into complex systems beyond traditional entropy measures.

Keywords:
combinatorial analysisdifferential equationsentropyequilibrium analysisfunctional measuresinformation dynamicsinformation theoryprobability distributions

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Area of Science:

  • Information Theory
  • Complex Systems Analysis
  • Probability Theory

Background:

  • Scalar measures like Shannon entropy provide limited insights into information dynamics.
  • Characterizing information dispersion across probability distributions is crucial for understanding complex systems.

Purpose of the Study:

  • Introduce derangetropy, a novel functional measure for information dynamics.
  • Characterize the dispersion of information within probability distributions.
  • Provide a new analytical tool for complex and hierarchical systems.

Main Methods:

  • Developed a functional measure, derangetropy, incorporating self-referential and periodic properties.
  • Utilized combinatorial justifications for theoretical underpinnings.
  • Performed empirical analysis to demonstrate utility.

Main Results:

  • Derangetropy offers a functional representation of information dispersion, unlike scalar entropy measures.
  • The measure provides insights into information dynamics governed by differential equations and equilibrium states.
  • Empirical analysis confirmed derangetropy's effectiveness in depicting distribution behavior and evolution.

Conclusions:

  • Derangetropy is a novel and powerful tool for analyzing information dynamics in probability distributions.
  • It enhances the study of complex and hierarchical systems by capturing information dispersion.
  • This functional measure complements existing scalar information-theoretic tools.