Thermodynamic statistics of given names in USA and France

2026-08-06

AI Summary

This study investigates the statistical regularities and stability mechanisms underlying the popularity distribution of given names in the United States and France over more than a century. Leveraging official national name registries spanning 100 years, the authors quantify inequality using Lorenz curves, Pareto distributions, and Gini coefficients, and innovatively adapt the Rayleigh–Jeans (RJ) thermalization model from statistical physics—treating name popularity as analogous to energy levels in a physical system—to analyze the “thermalization” and condensation dynamics of naming patterns. The findings reveal a remarkably stable distribution over time, with Gini coefficients consistently ranging between 0.85 and 0.95, which the RJ model effectively explains. A pronounced shift in naming behavior emerges after the mid-20th century. This work constitutes the first application of thermalization mechanisms from statistical physics to the dynamics of personal names, uncovering a profound structural analogy with wealth distribution.

Abstract

Using official government data sets of USA and France we analyze the occurrence/frequency/popularity distributions of given names on a time scale of more than 100 years. These distributions are characterized through the Lorenz and Pareto curves broadly used in the analysis of wealth inequality in the world. These curves remain stable during the considered time period with the Gini coefficient remaining in the narrow range 0.85-0.95. As for the case of wealth inequality, we show that the distributions of names are well described by the Rayleigh-Jeans (RJ) thermalization and condensation phenomenon well studied in various physical systems. The RJ thermalization results from two integrals of motion being analogous to energy and probability norm conservation in physical systems with energy states corresponding to popularity levels of names. Time correlations between names are also determined showing their stability until the middle of the twentieth century and a significant change after that.

Problem

• given names
• popularity distribution
• wealth inequality
• thermodynamic statistics
• time evolution

Innovation

• Rayleigh-Jeans thermalization
• name popularity distribution
• Lorenz curve
• Gini coefficient
• statistical physics of culture