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A theory for non-equilibrium systems is derived from a maximum entropyapproach similar in spirit to the equilibrium theory given by Gibbs. RequiringHamilton's principle of stationary action to be satisfied on average during atrajectory, we add constraints on the transition probability distribution whichlead to a path probability of the Onsager-Machlup form. Additional constraintsderived from energy and momentum conservation laws then introduce heat exchangeand external driving forces into the system, with Lagrange multipliers relatedto the temperature and pressure of an external thermostatic system. The resultis a fully time-dependent, non-local description of a nonequilibrium ensemble.Detailed accounting of the energy exchange and the change in informationentropy of the central system then provides a description of the entropyproduction which is not dependent on the specification or existence of asteady-state or on any definition of thermostatic variables for the centralsystem. These results are connected to the literature by showing a method forpath re-weighting, creation of arbitrary fluctuation theorems, and by providinga simple derivation of Jarzynski relations referencing a steady-state. Inaddition, we identify path free energy and entropy (caliber) functionals whichgenerate a first law of nonequilibrium thermodynamics by relating changes inthe driving forces to changes in path averages. Analogous to the Gibbsrelations, the variations in the path averages yield fluctuation-dissipationtheorems. The thermodynamic entropy production can also be stated in terms ofthe caliber functional, resulting in a simple proof of our microscopic form forthe Clausius statement. We find that the maximum entropy route provides a clearderivation of the path free energy functional, path-integral, Langevin,Brownian, and Fokker-Planck statements of nonequilibrium processes.

journal of physics. conference series

A First and Second Law for Nonequilibrium Thermodynamics: Maximum  Entropy Derivation of the Fluctuation-Dissipation Theorem and Entropy  Production Functionals