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Gintropy: Gini Index Based Generalization of Entropy.

Tamás S Biró1,2, Zoltán Néda3

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|December 8, 2020
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Summary
This summary is machine-generated.

This study reveals mathematical links between entropy and the Gini index, introducing a new measure for socio-economic complexity. This work generalizes Gibbs-Boltzmann-Shannon entropy using Lorenz curve transformations for broader applications.

Keywords:
Gini indexeconophysicsentropysocio-economic inequalities

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Area of Science:

  • Interdisciplinary science
  • Statistical mechanics
  • Econophysics
  • Sociophysics

Background:

  • Entropy quantifies information, equilibration, and probability in physics and informatics.
  • The Gini index measures social and economic inequality.
  • Existing measures lack a unified framework for complexity across disciplines.

Purpose of the Study:

  • To explore mathematical connections between entropy and the Gini index.
  • To introduce a novel measure linking these concepts.
  • To support a generalized entropy framework for socio-economic complexity.

Main Methods:

  • Mathematical analysis of entropy and Gini index properties.
  • Development of a new quantitative measure based on Lorenz curve transformations.
  • Application of generalized Gibbs-Boltzmann-Shannon entropy.

Main Results:

  • Identified significant mathematical similarities between entropy and the Gini index.
  • Introduced a novel measure demonstrating an analogy between information theory and inequality.
  • Validated a generalized entropy approach for quantifying socio-economic complexity.

Conclusions:

  • A generalized entropy, derived from Lorenz curve transformations, offers a unified perspective.
  • This framework effectively quantifies complexity in socio- and econo-physics.
  • The findings bridge concepts from information theory and social sciences.