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 of connecting 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.

中文翻译：

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Gintropy：基于基尼指数的熵概括


熵被用于物理、数学、信息学和相关领域来描述平衡、耗散、最大概率状态和信息的最佳压缩。另一方面，基尼指数是社会中社会和经济不平等的既定衡量标准。在本文中，我们探讨了这两个量的数学相似性和联系，并引入了一种新的度量，能够在有趣的类比层面上连接这两个量。这支持了这样的观点：基于洛伦兹曲线的变换，吉布斯-玻尔兹曼-香农熵的推广可以适当地用于量化社会物理学和经济物理学中复杂性的不同方面。