Thermodynamic description of world GDP distribution over countries

ArXiv ID: 2512.06420 “View on arXiv”

Authors: Klaus M. Frahm, Dima L. Shepelyansky

Abstract

We apply the concept of Rayleigh-Jeans thermalization of classical fields for a description of the world Gross Domestic Product (GDP) distribution over countries. The thermalization appears due to a variety of interactions between countries with conservation of two integrals being total GDP and probability (norm). In such a case there is an emergence of Rayleigh-Jeans condensation at states with low GDP. This phenomenon has been studied theoretically and experimentally in multimode optical fibers and we argue that it is at the origin of emergence of poverty and oligarchic phases for GDP of countries. A similar phenomenon has been discussed recently in the framework of the Wealth Thermalization Hypothesis to explain the high inequality of wealth distribution in human society and companies at Stock Exchange markets. We show that the Rayleigh-Jeans thermalization well describes the GDP distribution during the last 50 years.

Keywords: Thermalization, Rayleigh-Jeans Condensation, Economics of Poverty, GDP Distribution, Statistical Physics, Macroeconomics

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical physics concepts (Rayleigh-Jeans thermalization, condensation) and mathematical modeling (implicit equations, Lorenz curves) with multiple parameter fits, yet the empirical component is substantial, analyzing 50 years of global GDP data from public sources (UN, IMF, World Bank) and comparing two theoretical models (RJS/RJE) to real-world distributions, though lacking backtesting or executable code.

  flowchart TD
    A["Research Goal<br>Model world GDP distribution<br>using statistical physics"] --> B["Key Methodology<br>Apply Rayleigh-Jeans thermalization"]
    
    B --> C["Data Inputs<br>World GDP data over last 50 years"]
    
    C --> D["Computational Process<br>Thermalization with conservation of<br>Total GDP and Probability (norm)"]
    
    D --> E["Computational Process<br>Identify emergence of<br>Rayleigh-Jeans condensation"]
    
    E --> F["Key Finding 1<br>Emergence of poverty phase<br>(low GDP condensate)"]
    
    E --> G["Key Finding 2<br>Emergence of oligarchic phase<br>(high GDP states)"]
    
    F --> H["Outcome<br>Model validates against<br>50 years of GDP data"]
    G --> H