The emergence of socio-economic structure: a first-principles kinetic theory

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.