Contribution to Statistical Mechanics far from Equilibrium. II: Extension to Non-Steady States and to General Stochastic Models

Abstract

The new approach to non-equilibrium statistical mechanics initiated in Part I of this series is extended to cover non-steady states as well as more general stochastic models. The logarithm of the solution to the stochastic equation for the probability distribution function of gross variables is obtained as a systematic perturbation series starting from the logarithm of the suitably defined Gaussian part of the local equilibrium distribution function, which is best expressed in terms of the characteristic function of the probability distribution function. Again the effects of heat baths which surround the system enter only on the level of fully renormalized macroscopic equations of motion. A self-consistent scheme was derived which determines the macroscopic law of evolution and the probability distribution function of fluctuations.