The Emergence of Socio-Economic Structure: A First-Principles Kinetic Theory

TL;DR

This paper develops a kinetic theory framework linking individual agent behaviors governed by Langevin dynamics to macro-scale societal phenomena like urban concentration and wealth inequality, revealing the role of resource heterogeneity.

Contribution

It introduces a first-principles kinetic theory approach that derives macro societal patterns from microscopic agent models, bridging micro-macro gaps in social science modeling.

Findings

Derivation of mesoscopic Dean-Kawasaki dynamics from agent behavior.

Exact macroscopic Vlasov-Fokker-Planck equations for societal patterns.

Heterogeneous resources alone can generate spatial and economic inequalities.

Abstract

Bridging the gap between individual agent behavior and macroscopic societal patterns is a central challenge in the social sciences. In this work, we propose a solution to this problem via a kinetic theory formulation. We demonstrate that complex, empirically-observed phenomena, such as the concentration of populations in cities and the emergence of power-law wealth distributions, can be derived directly from a microscopic model of agents governed by underdamped Langevin dynamics. Our multi-scale derivation yields the exact mesoscopic fluctuating (Dean-Kawasaki) dynamics and the macroscopic Vlasov-Fokker-Planck system of equations. The analytical solution of this system reveals how a heterogeneous resource landscape alone is sufficient to generate the coupled structures of spatial and economic inequality, thus providing a formal link between micro-level stochasticity and macro-level deterministic order.