Contributions to Statistical Mechanics Far from Equilibrium. I: Treatment of a Stochastic Model

Abstract

A new approach to steady non-equilibrium state is presented for a system described by a stochastic equation for the probability distribution function of the gross variables. The use of the second quantization representation permits exploitation of the methods developed in quantum theories of many-body systems and interacting fields, and in particular, the problem of obtaining the steady state distribution function from the local equilibrium distribution function reduces to that of finding the true vacuum state from the free vacuum state in quantum theory of interacting fields. The approach naturally leads to the introduction of the boundary condition representing contacts with heat reservoirs in a way completely independent of the irrelevant details of the nature of the contacts. The important role played by nonlinear coupling among the gross variables in obtaining steady state distribution is stressed, where renormalization of transport coefficients also enters in a natural way.