Dynamic mean field models: H-theorem for stochastic processes and basins of attraction of stationary processes

Stochastic processes of dynamic mean field models are studied in terms of nonlinear Fokker–Planck equations. We show that H-theorems for single time-point distributions can be used to derive H-theorems for hierarchies of joint distributions. In doing so, we prove the convergence of transient stochastic processes to stationary ones. For multistable systems we furthermore determine the basins of attraction of these stationary processes. Our results are illustrated by means of a mean field model exhibiting bistability.