Contributions to Statistical Mechanics Far from Equilibrium. III: Non-Perturbative Method for Steady States

Abstract

The systematic perturbation scheme for solving stochastic equations for the distribution function of gross variables described in earlier publications of this series is used to develop a non-perturbative self-consistent method for obtaining average values of the gross variables, time correlation functions of fluctuations, non-equilibrium steady state distribution function and the response function to an external disturbance. The analogy of the present problem with that of condensed Bose systems is found to be helpful, and the method requires two kinds of renormalized propagators and three kinds of renormalized vertices to be determined self-consistently. The formalism of Martin, Rose and Siggia on the same problem comes out rather naturally in our approach without introducing their unfamiliar operator. The problem can be simplified so that only one type of propagators and one type of vertices appear if the steady state distribution function is Gaussian.