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Gintropy: Gini index based generalization of Entropy

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  • Tam'as S. Bir'o
  • Zolt'an N'eda

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.

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  • Tam'as S. Bir'o & Zolt'an N'eda, 2020. "Gintropy: Gini index based generalization of Entropy," Papers 2007.04829, arXiv.org.
    • Handle: RePEc:arx:papers:2007.04829
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    1. Luerssen, Christoph & Gandhi, Oktoviano & Reindl, Thomas & Sekhar, Chandra & Cheong, David, 2020. "Life cycle cost analysis (LCCA) of PV-powered cooling systems with thermal energy and battery storage for off-grid applications," Applied Energy, Elsevier, vol. 273(C).
    2. Biró, Tamás S. & Telcs, András & Józsa, Máté & Néda, Zoltán, 2023. "Gintropic scaling of scientometric indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    3. Joseph, Bijin & Chakrabarti, Bikas K., 2022. "Variation of Gini and Kolkata indices with saving propensity in the Kinetic Exchange model of wealth distribution: An analytical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    4. Ghosh, Asim & Chakrabarti, Bikas K., 2021. "Limiting value of the Kolkata index for social inequality and a possible social constant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

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