A Quantum Field Perspective on Income Inequality and Wealth Concentration: Entropy Dynamics, Phase Transitions, and Redistribution in a Panel of 100 Economies, 1985--2025

This paper develops and estimates a quantum field theory (QFT)-informed framework for interpreting income inequality dynamics as a manifestation of wealth field interactions, symmetry breaking, and entropy dispersion across economic space. Departing from—but building upon—the established econophysics literature on Boltzmann-Gibbs and Pareto wealth distributions, we introduce a scalar wealth field $\phi(x,t)$ governed by a Lagrangian density with a double-well potential capable of generating inequality traps as spontaneous symmetry-breaking equilibria. This theoretical extension is motivated by three empirical observations that remain incompletely explained by existing frameworks: (i)~sudden, non-gradual wealth concentration episodes; (ii)~persistent inequality traps in developing economies; and (iii)~strongly asymmetric responses of inequality to redistribution shocks. Using an unbalanced panel of 100 developed and developing economies spanning 1985--2025 (up to 4,100 country-year observations), we estimate Pareto exponents via maximum likelihood, fit Boltzmann-Gibbs temperature parameters via moment matching, and test the QFT-augmented panel quantile regression specification against conventional panel fixed-effects and GMM baselines. Driscoll--Kraay standard errors account for cross-sectional dependence and temporal autocorrelation. Our main findings are: (i) the Pareto exponent has declined from approximately 2.84 (developed economies, 1985--1994) to 1.71 (developing economies, 2015--2025), indicating intensifying fat tails in the upper wealth distribution; (ii) the QFT wealth field potential exhibits double-well structure in high-inequality economies, consistent with symmetry-breaking inequality traps; (iii) a one-unit increase in the wealth field potential is associated with a 0.288 point increase in the Gini coefficient (FE estimate), while financial openness and capital income share amplify concentration; and (iv) panel quantile regressions reveal strongly heterogeneous effects, with the wealth field potential coefficient rising monotonically from 0.211 at the10 percentile to 0.388 at the 90, implying larger field effects precisely where inequality is already highest. These findings contribute to the literature by providing a unified theoretical framework that nests Boltzmann-Gibbs, Pareto, and field-theoretic approaches as special cases, and by delivering the first large-panel empirical evaluation of wealth field dynamics across both developed and developing economies.