Symmetry, Entropy, Diversity and (Why Not?) Quantum Statistics in Society

Abstract

We describe society as an out-of-equilibrium probabilistic system: Individuals occupy resource states in it and produce entropy over definite time periods. Resulting thermodynamics is however unusual because a second entropy, , measures inequality or diversitya typically social featurein 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 : expectedly, and , and new ones, diversity and interactions between individuals; the latter are determined by the 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 number 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 classes of equivalence that happen to coincide with acceptable definitions of social classes or periods in human life. The entropy is non-extensive and obtainable from data. Theoretical laws are compared to empirical ones in four different cases of economic or physiological diversity. Acceptable fits are found for all of them.

Fermion-like behavior of elements/agents in their spatial distribution around points of interest

“…It is worth explicitly noting here that a simple exponential decay such as the one stemming from a classical Boltzmann distribution would clearly not describe the data in Figures 3b and 5b. The application of quantum statistics is not so widespread although some other recent examples can be found related to social and economical systems [15,16]. The type of systems described in the present work can be clearly modeled with a fermion-like statistics providing at the same time a highly illustrative and interesting application of it.…”