Fluctuations and nonlinear irreversible processes

Abstract

The paper reexamines the relationship between fluctuations and nonlinear irreversible processes. The deterministic equations for nonlinear irreversible processes are shown to be derivable from a minimum principle, which permits the introduction of a set of variables $\eta$ canonically conjugate to the macroscopic variables $a$. In terms of the action integral of the minimum principle and the conjugate variables $\eta$, we are able to construct a covariant expression for the conditional probability of the fluctuations for a small interval of time. The short-time conditional probability is used to construct the conditional probability for finite times as a path integral. This path integral is a generalization of a corresponding expression of Onsager and Machlup for the linear regime. An explanation for a difference with Graham's recent calculation is given. The conditional probability is shown to satisfy a Fokker-Planck equation, which has the form derived from statistical mechanics by one of us.