Thermodynamic theory of voting and EU elections

2026-07-16

AI Summary

This study investigates the common statistical mechanisms underlying party vote shares in European Union elections and socioeconomic wealth inequality through the lens of statistical physics. By analogizing vote allocation to energy distribution in a system of coupled nonlinear oscillators, the authors introduce—under constraints of total energy and probability conservation—a Rayleigh–Jeans thermalization framework to characterize condensation phenomena in low-energy voting states. This approach innovatively integrates constraint-driven condensation with classical thermodynamic theory, successfully fitting both Lorenz and Pareto curves observed in EU electoral data. Moreover, it accurately reproduces the discrete vote-share distribution among candidates in the first round of the French presidential election, thereby revealing a shared statistical-mechanical origin between collective voting behavior and wealth distribution.

Abstract

We introduce a thermodynamic theory of voting and show that it provides a good description of distribution of party votes in EU elections. The theory traces parallels between system energies of coupled nonlinear oscillators and party vote fractions. Such a classical system evolution is characterized by the conservation of total energy and probability norm that leads to the Rayleigh-Jeans (RJ) thermalization and condensation at low energy states. A similar thermalization also describes the wealth inequality in society. This feature belongs to the phenomena of constraint driven condensation known in statistical mechanics. We show that the RJ theory well depicts the Lorenz and Pareto curves obtained from the EU vote results. The theory also recovers the dispersion of votes between candidates of first round presidential elections in France.

Problem

• voting distribution
• thermodynamic theory
• Rayleigh-Jeans thermalization
• constraint-driven condensation
• EU elections

Innovation

• thermodynamic theory of voting
• Rayleigh-Jeans thermalization
• constraint-driven condensation
• Lorenz curve
• Pareto distribution