Gravity Analog Model of Non-equilibrium Thermodynamics

Abstract

Non-equilibrium thermodynamics of Onsager and Machlup and of Hashitsume is reformulated as a gravity analog model, in which thermodynamic variables, kinetic coefficients and generalized forces form, respectively, coordinates, metric tensor and vector fields in a space of thermodynamic variables. The relevant symmetry of the model is the general coordinate transformation. Then, the entropy production is classified into three categories, when a closed path is depicted as a thermodynamic cycle. One category is time reversal odd, and is attributed to the number of lines of magnetic flux passing through the closed path, having monopole as a source. There are two time reversal even categories, one of which is attributed to the space curvature around the path, having gravitational instanton as a source, which dominates for a rapid operation of the cycle. The last category is the usual one, which remains even for the quasi-equilibrium operation. It is possible to extend the model to include non-linear responses. In introducing new terms, important is the dimensional counting, using two parameters, the temperature and the relaxation time. The effective action, being induced by the non-equilibrium thermodynamics, is derived. This is a candidate for the action which controls the dynamics of kinetic coefficients and thermodynamic forces. An example is given in a chemical oscillatory reaction in a solvent of the van der Waals type. Fluctuation-dissipation theorem is examined `a la Onsager, and a derivation of the gravity analog thermodynamic model from quantum mechanics is sketched, based on an analogy to the resonance problem.