Wealth Thermalization Hypothesis and Social Networks
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.
Related
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- Predicting dynamics from flows of the eigenstate thermalization hypothesis
- The Multi-trace Eigenstate Thermalization Hypothesis
- Dynamical thermalization and turbulence in social stratification models
- Social networks, confirmation bias and shock elections
BibTeX
@article{frahm2026wealth,
title = {{Wealth Thermalization Hypothesis and Social Networks}},
author = {Klaus M. Frahm and Dima Shepelyansky},
journal = {Journal of Statistical Physics},
year = {2026},
month = may,
doi = {10.1007/s10955-026-03621-2},
url = {https://hal.science/hal-05735730v1},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Wealth Thermalization Hypothesis and Social Networks
AU - Klaus M. Frahm
AU - Dima Shepelyansky
PY - 2026
DA - 2026/05/27
JO - Journal of Statistical Physics
DO - 10.1007/s10955-026-03621-2
UR - https://hal.science/hal-05735730v1
AB - 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.
SN - 0022-4715
SN - 1572-9613
ER -