Information geometrical characterization of the Onsager-Machlup process

Abstract

The Onsager-Machlup (OM) relaxation process, which provides a prototypical example of linear nonequilibrium thermodynamics, is characterized in terms of information geometry over the two-dimensional temperature-time parameter space. After deriving the probability distribution function for the OM process under the harmonic potential within a theoretical framework based on a transformation into imaginary-time quantum mechanics, the Fisher information metric is explicitly obtained. Differential geometry in the temperature-time space then gives the scalar curvature R=-1, thus specifying the OM process in a topological manner.