Non-equilibrium potentials and stationary probability distributions of some dissipative models without manifest detailed balance

Abstract

Practical methods are developed to analyze the steady state probability distributions of dynamical Fokker-Planck models without manifest detailed balance in the limit of small noise. We consider two different models, whose deterministic attractor is a fixed point at the origin, and construct the leading terms of systematic expansions in various small parameters of the “non-equilibrium potential” and the stationary probability distribution of the models.