Dynamical thermalization and turbulence in social stratification models

2026-03-25

AI Summary

This study investigates the chaotic dynamics, wealth inequality, and energy transport mechanisms arising from nonlinear interactions within social stratification systems. By constructing a network of Hamiltonian oscillators coupled through social ties and incorporating energy (wealth) stratification alongside nonlinear coupling, the work pioneers the application of Rayleigh–Jeans thermalization theory and the Kolmogorov–Zakharov wave turbulence framework to social modeling. The analysis reveals that above a critical chaos threshold, the system approaches a Rayleigh–Jeans distribution, accompanied by condensation in low-energy states—analogous to extreme wealth concentration in real societies. Under external energy pumping, the system exhibits canonical wave turbulence characteristics. This research establishes a novel paradigm rooted in nonlinear dynamics and statistical physics for understanding the dynamical origins of wealth inequality.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Application Domains: Humanities & Computational Social Science

Application Category

• Social Networks and Social Media: Computational social science
• Economics, Online Markets and Human Computation: Social networks and social learning
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• social stratification
• dynamical thermalization
• wealth inequality
• nonlinear dynamics
• turbulence

Innovation

• dynamical thermalization
• social stratification
• Rayleigh-Jeans condensation
• nonlinear wave turbulence
• Hamiltonian chaos