Wealth Thermalization Hypothesis and Social Networks

ArXiv ID: 2506.17720 “View on arXiv”

Authors: Klaus M. Frahm, Dima L. Shepelyansky

Abstract

In 1955 Fermi, Pasta, Ulam and Tsingou performed first numerical studies with the aim to obtain the thermalization in a chain of nonlinear oscillators from dynamical equations of motion. This model happend to have several specific features and the dynamical thermalization was established only later in other studies. In this work we study more generic models based on Random Matrix Theory and social networks with a nonlinear perturbation leading to dynamical thermalization above a certain chaos border. These systems have two integrals of motion being total energy and norm so that the theoretical Rayleigh-Jeans thermal distribution depends on temperature and chemical potential. We introduce the wealth thermalization hypothesis according to which the society wealth is associated with energy in the Rayleigh-Jeans distribution. At relatively small values of total wealth or energy there is a formation of the Rayleigh-Jeans condensate, well studied in physical systems such as multimode optical fibers. This condensation leads to a huge fraction of poor households at low wealth and a small oligarchic fraction which monopolizes a dominant fraction of total wealth thus generating a strong inequality in human society. We show that this thermalization gives a good description of real data of Lorenz curves of US, UK, the whole world and capitalization of companies at Stock Exchange of New York SE (NYSE), London and Hong Kong. It is also shown that above a chaos border the dynamical Rayleigh-Jeans thermalization takes place also in social networks with the Lorenz curves being similar to those of wealth distribution in world countries. Possible actions for inequality reduction are briefly discussed.

Keywords: Random Matrix Theory, Rayleigh-Jeans Distribution, Wealth Condensation, Lorenz Curve, Thermalization, Economics / Wealth Distribution

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper uses advanced concepts from nonlinear dynamics, random matrix theory, and statistical physics (Rayleigh-Jeans distribution, condensation, chaos borders), which constitutes high mathematical density. It also presents fits to real-world data (Lorenz curves for countries, stock exchange capitalizations) and draws empirical conclusions from these comparisons, indicating substantial empirical rigor.

  flowchart TD
    A["<b>Research Goal</b><br/>Explain wealth inequality via<br/>dynamical thermalization models"] --> B
    B["<b>Methodology</b><br/>Random Matrix Theory +<br/>Nonlinear perturbation"] --> C
    C["<b>Inputs</b><br/>Lorenz curves (US, UK, World)<br/>Stock market capitalizations"] --> D
    D["<b>Computation</b><br/>Dynamical Rayleigh-Jeans<br/>distribution analysis"] --> E
    E["<b>Key Finding 1</b><br/>Wealth Condensation<br/>Rayleigh-Jeans condensate forms<br/>(Oligarchic fraction)"] --> F
    F["<b>Key Finding 2</b><br/>Social Networks<br/>Similar inequality patterns<br/>above chaos border"] --> G
    G["<b>Outcome</b><br/>Hypothesis validated<br/>Mechanism for inequality reduction<br/>identified"]