Properties of Nonequilibrium Steady States: a Path Integral Approach
  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 those 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. 
E.G.D. Cohen