Properties of nonequilibrium steady states: a path integral approach

Abstract

A number of properties of systems in a nonequilibrium steady state (NESS) areinvestigated by a generalization of the Onsager–Machlup (OM) path integral approach forsystems in an equilibrium state (ES). A thermodynamics formally identical to that in anES can be formulated, but with definitions of work and heat as needed to maintain theNESS. In this approach, the heat plays a crucial role and is directly related to the differentbehavior of a system’s forward and backward paths in time in an appropriate functionspace. However, an ambiguity in the choice of the time-backward path corresponding to agiven time-forward path prevents a unique general formal theory for systems in aNESS. Unique unambiguous physically acceptable physical results for a system in aNESS appear to be obtainable only after specifying the physical nonequilibriumparameters, which define a system in a NESS as part of a larger system. NESSsystems are therefore fundamentally different from those in an ES. Furthermore, anexample is given for a particular system that the fluctuations of a system in aNESS behave in many respects very differently from those in a system in anES.