The unified geometric theory of mesoscopic stochastic pumps and reversible ratchets

Abstract

We construct a unifying theory of geometric effects in mesoscopic stochastic kinetics. We demonstrate that the adiabatic pump and the reversible ratchet effects, as well as similar new phenomena in other domains, such as in epidemiology, all follow from geometric phase contributions to the effective action in the stochastic path integral representation of the moment generating function. The theory provides the universal technique for identification, prediction and calculation of pump-like phenomena in an arbitrary mesoscopic stochastic framework.