Microscopic basis for Onsager-Machlup theory

The phenomenological Langevin equation in the theory of Onsager-Machlup (OM) is derived from a microscopic theory based on the closed time path generating functional formalism. Following the theory of Wakou-Koide-Fukuda (WKF) we derive the general form of the Langevin equation and carry out the adiabatic expansion. Then, at first order in the adiabatic expansion, the Langevin equation of OM type is naturally derived. In the course of the derivation, the theory of WKF is extended to the multi-macrovariable case, which is defined as the space average of arbitrary operators. The method of adiabatic expansion is made more systematic by using the inversion formula. We proceed to second order in the adiabatic expansion and show that the Langevin equation extended by Machlup-Onsager is obtained.