Gintropy: Gini index based generalization of Entropy

TL;DR

This paper introduces Gintropy, a new measure connecting entropy and Gini index, to better quantify complexity in socio- and econo-physics by generalizing entropy through Lorenz curve transformations.

Contribution

It proposes a novel measure called Gintropy that unifies entropy and Gini index, enabling new insights into complexity in socio-economic systems.

Findings

Gintropy links entropy and Gini index mathematically.

Supports a generalized entropy framework for socio- and econo-physics.

Provides a new tool for analyzing inequalities and complexity.

Abstract

Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established measure for social and economical inequalities in a society. In this paper we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable to connect these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs--Boltzmann--Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.