Variational approach to KPZ: Fluctuation theorems and large deviation function for entropy production

Abstract

Motivated by the time behavior of the functional arising in the variational approach to the Kardar-Parisi-Zhang (KPZ) equation, and in order to study fluctuation theorems in such a system, we have adapted a path-integral scheme that adequately fits to this kind of study dealing with unstable systems. As the KPZ system has no stationary probability distribution, we show how to proceed for obtaining detailed as well as integral fluctuation theorems. This path-integral methodology, together with the variational approach, in addition to allowing analyze fluctuation theorems, can be exploited to determine a large deviation function for entropy production. Nonequilibrium systems have attracted a growing research interest during the last decades. Among the many aspects, there are two that have been extensively studied. On the one hand, there is the paradigmatic Kardar-Parisi-Zhang (KPZ) model that describes the growth of rough surfaces for out-of equilibrium extended systems. On the other hand, there is stochastic thermodynamics that intends to describe, exploiting stochastic variables, the non-equilibrium dynamics present in microscopic as well as mesoscopic systems. Here, both aspects have been integrated in order to analyze the first from the point of view of the second. It is shown how the variational approach of the KPZ system allows one to readily obtain fluctuation theorems as well as information about the large deviation function for the entropy production. It is expected that such an approach could offer alternative information about critical exponents for the KPZ universality class.