Biró Tamás S, Néda Zoltán
Wigner Research Centre for Physics, 1121 Budapest, Hungary.
Complexity Science Hub, 1080 Vienna, Austria.
Entropy (Basel). 2020 Aug 10;22(8):879. doi: 10.3390/e22080879.
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.
熵在物理学、数学、信息学及相关领域中用于描述平衡、耗散、最大概率状态和信息的最优压缩。另一方面，基尼指数是衡量社会中社会和经济不平等程度的既定指标。在本文中，我们探讨了这两个量在数学上的相似性和联系，并引入了一种新的度量方法，该方法能够在一个有趣的类比层面上连接这两者。这支持了这样一种观点，即基于洛伦兹曲线变换的吉布斯 - 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。
