Derangetropy in Probability Distributions and Information Dynamics

TL;DR

This paper introduces derangetropy, a new functional measure for analyzing information dynamics in probability distributions, offering deeper insights than traditional scalar measures like Shannon entropy.

Contribution

It presents derangetropy as a novel functional measure that captures the dispersion and evolution of information across distributions, with theoretical and empirical validation.

Findings

Derangetropy effectively characterizes distribution behavior.

It reveals deeper insights into information dynamics.

The measure is useful for complex and hierarchical systems.

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.