Symmetry, Entropy, Diversity and (why not?) Quantum Statistics in Society

TL;DR

This paper models society as a nonequilibrium probabilistic system using thermodynamic concepts like entropy and symmetry, revealing phase transitions and statistical behaviors akin to quantum physics, with empirical validation across diverse data sets.

Contribution

It introduces a novel thermodynamic framework for social systems, incorporating social diversity and interactions, and applies quantum statistical models to explain societal resource distributions.

Findings

Identifies a symmetry phase transition at Gini 1/3.

Fits empirical data with Fermi-Dirac and Bose-Einstein statistics.

Demonstrates non-extensive entropy in social data.

Abstract

We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a typically social feature, inequality or diversity in the distribution of available resources. A symmetry phase transition takes place at Gini values 1/3, where realistic distributions become asymmetric. Four constraints act on S: expectedly, N and W, and new ones, diversity and interactions between individuals; the latter result from the two coordinates of a single point in the data, the peak. The occupation number of a job is either zero or one, suggesting Fermi-Dirac statistics for employment. Contrariwise, an indefinite nujmber of individuals can occupy a state defined as a quantile of income or of age, so Bose-Einstein statistics may be required. Indistinguishability rather than anonymity of individuals and resources is thus needed. Interactions between individuals define define classes of equivalence that happen to coincide with acceptable definitions of social classes or periods in human life. The entropy S is non-extensive and obtainable from data. Theoretical laws are compared to data in four different cases of economical or physiological diversity. Acceptable fits are found for all of them.