Bistable systems: Master equation versus Fokker-Planck modeling

Abstract

Relaxation and fluctuations of nonlinear macroscopic systems, which are frequently described by means of Fokker-Planck or Langevin equations, are studied on the basis of a master equation. The problem of an approximate Fokker-Planck modeling of the dynamics is investigated. A new Fokker-Planck modeling is presented which is superior to the conventional method based on the truncated Kramers-Moyal expansion. The new approach is shown to give the correct transition rates between deterministically stable states, while the conventional method overestimates these rates. An application to the Schl\"ogl models for first- and second-order nonequilibrium phase transitions is given.