The Path Probability Ansatz and Master Equation

Abstract

A trial is made of a quasi-stochastic approach to the non-equilibrium statistical mechanics on the basis of Kikuchi's path probability ansatz. In a state arbitrarily away from thermal equilibrium, the general Baye's rule is derived in which the transition probability explicitly involves a time-dependent Hamiltonian and particle number. This newly derived transition probability is utilized to obtain the mesoscopic master equation, and thus, the Fokker-Planck equation which is reinterpreted in terms of a set of canonical coordinates. One of other applications is the production rate of dynamical path entropy, being made up of the internal entropy production rate and absorption rate of free energy out of the environment. The many-particle hoppings are also investigated by the field theoretical approach