The definition of entropy in non-equilibrium states

Abstract

Several different expressions are used in statistical mechanics for the entropy. They are here evaluated explicitly for non-equilibrium states. The result consists of three terms: (i) the equilibrium entropy; (ii) the familiar quadratic term measuring the departure from equilibrium; (iii) a term referring to the fluctuations. Only the last term differs for the several expressions for the entropy. However, it is much smaller than the second term when the departure from equilibrium is large compared to the size of the fluctuations.