Dynamical thermalization and turbulence in social stratification models

TL;DR

This paper models social stratification using nonlinear oscillator networks, revealing chaotic dynamics that lead to thermalization and wealth distribution patterns similar to real-world inequality, with turbulence phenomena observed under energy exchange conditions.

Contribution

It introduces a novel nonlinear oscillator model for social stratification, demonstrating chaotic dynamics, thermalization, and turbulence phenomena relevant to wealth distribution.

Findings

Chaotic dynamics induce thermalization with Rayleigh-Jeans distribution.

Low-energy states exhibit condensation akin to wealth inequality.

Energy pumping leads to turbulence-like behavior in the system.

Abstract

We study the nonlinear chaotic dynamics in a system of linear oscillators coupled by social network links with an additional stratification of oscillator energies, or frequencies, and supplementary nonlinear interactions. It is argued that this system can be viewed as a model of social stratification in a society with nonlinear interacting agents with energies playing a role of wealth states of society. The Hamiltonian evolution is characterized by two integrals of motion being energy and probability norm. Above a certain chaos border the chaotic dynamics leads to dynamical thermalization with the Rayleigh-Jeans (RJ) distribution over states with given energy or wealth. At low energies, this distribution has RJ condensation of norm at low energy modes. We point out a similarity of this condensation with the wealth inequality in the world countries where about a half of population owns only a couple of percent of the total wealth. In the presence of energy pumping and absorption, the system reveals features of the Kolmogorov-Zakharov turbulence of nonlinear waves.