Entropy production in nonequilibrium systems described by a Fokker-Planck equation

We study the entropy production in nonequilibrium systems described by a Fokker-Planck equation. We have devised an expression for the entropy flux in the stationary state. We have found that he entropy flux can be written as an ensemble average of an expression containing the force and its derivative. This result is similar to the one used by Lebowitz and Spohn for system following a Markovian process in discrete space. We have also been able to obtain a fluctuation-dissipation type relation between the dissipated power, which was written as an ensemble average, and the production of entropy for the case of systems in contact with one heat bath. We have applied the results for a simple model for particles subjected to dissipative forces.