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Gintropy: Gini Index Based Generalization of Entropy.
Tamás S Biró1,2, Zoltán Néda3
1Wigner Research Centre for Physics, 1121 Budapest, Hungary.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
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.
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.
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