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