Paper: arXiv 2603.24190

Authors: Klaus M. Frahm, Dima L. Shepelyansky

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents an advanced Hamiltonian dynamics and wave turbulence model applied to social stratification and wealth distribution. While mathematically rich and conceptually novel, it completely lacks real-world empirical validation or quantitative backtesting against empirical economic datasets.

Research Flowchart

  flowchart TD
    A["Research Question: How do nonlinear coupled oscillators model social stratification & wealth inequality?"] --> B["System Setup: Oscillators on social networks with energy stratification & nonlinear interactions"]
    B --> C["Hamiltonian Dynamics Simulation: Track energy & norm conservation under pumping/absorption"]
    C --> D{"Energy Level & Pumping State"}
    D -- "Above Chaos Border" --> E["Outcome 1: Dynamical Thermalization via Rayleigh-Jeans Distribution"]
    D -- "Low Energies" --> F["Outcome 2: RJ Condensation mimicking real-world wealth inequality"]
    D -- "Pumping & Absorption" --> G["Outcome 3: Kolmogorov-Zakharov Wave Turbulence"]