Variational version of thermal conduction fluctuations in the context of the most probable route

Abstract

An expression for the square-law fluctuation of internal energy is obtained in the framework of the local equilibrium approach with the aid of the non-equilibrium distribution function presented by Zubarev (1974). It is shown that this fluctuation satisfies the necessary conditions for its use as Liapounov's function. It is demonstrated that Liapounov's stability requirement leads to a fluctuating functional which has a minimum for the hydrodynamic stage. The infinitesimality estimates of the right parts are found for two balance equations: energy and entropy. It is shown that the local potential of Prigogine and Glansdorff (1971) can be derived from perturbed fluctuating functional obtained here. With the aid of the well known formula of the Onsager-Machlup postulate for the density probability transition of a thermodynamic system from some non-equilibrium state, the path integrals are obtained for the evolution of the system in the hydrodynamic stage.