ONSAGER PRINCIPLE FROM LARGE DEVIATION POINT-OF-VIEW

If we interpret the macroscopic time derivatives as the time average of microscopic time derivatives, there is a natural large deviation theoretical framework associated with this average. It turns out that the accompanying rate function is the Onsager-Machlup Lagrangian (after introducing Gaussian approximation). Thus Onsager's principle has a large deviation theoretical interpretation, and seems to be an example of an apparently general principle that the rate function of microscopic dynamics governs the phenomenological time evolution of macroscopic quantities.