Extended local equilibrium approach to stochastic thermodynamics

A new approach to stochastic thermodynamics is developed, in which the local equilibrium hypothesis is extended to incorporate the effect of fluctuations. A fluctuating entropy in the form of a random functional of the fluctuating state variables is introduced, whose balance equation allows to identify the stochastic entropy flux and stochastic entropy production. The statistical properties of these quantities are analyzed and illustrated on representative examples.