Mean Field Limits for Stochastic, Underdamped Reactive Langevin Dynamics Models

Abstract: We rigorously derive the effective large-population, mean-field dynamics of particle-based reactive Langevin dynamics (PBRLD) models. These models extend particle-based stochastic reaction-diffusion (PBSRD) descriptions by incorporating velocities, inertial effects, and underdamped motion. In Isaacson, Liu, Spiliopoulos, and Yao, SIAP 2026, PBRLD models were formulated and shown to recover Doi volume reactivity PBSRD model in the overdamped limit. In this work we prove convergence of the associated measure-valued stochastic processes, representing species concentration fields on position-velocity phase space, to a deterministic mean-field limit. The limiting equations form a novel system of nonlocal kinetic reaction-diffusion partial integro-differential equations, coupling hypoelliptic transport with reaction terms that retain the spatial and velocity structure of the underlying particle interactions.