Stationary solution of master equations in the large-system-size limit

Abstract

To study the stationary probability distribution of master equations in the large-system-size limit, we introduce a kind of master Hamiltonian which is similar to the Fokker-Planck Hamiltonian suggested by Graham et al. in the study of Fokker-Planck equations in the weak-noise limit. The general procedure to associate the potential of the master equation with a certain separatrix of the master Hamiltonian system is described. With some solvable models we show how the smoothness of the potential of the master equation is related to the integrability of the corresponding master Hamiltonian system.