Fluctuations in Stochastic Interacting Particle Systems

Abstract

We discuss fluctuations in stochastic lattice gas models from a microscopic and mesoscopic perspective by using techniques from algebra, in particular the use of symmetries and time-reversal. First we present a generic method to derive rigorously duality functions. As applications we obtain detailed information about density fluctuations in the symmetric simple exclusion process on any graph and about the microscopic structure and fluctuations of shocks in the one-dimensional asymmetric simple exclusion process. Then we use time reversal to prove a general current fluctuation theorem from which celebrated fluctuation relations such as the Jarzynski relation and the Gallavotti-Cohen symmetry arise as corollaries and which can be straightforwardly generalized to derive other fluctuation relations. Finally, going beyond rigorous results, we describe briefly how nonlinear fluctuating hydrodynamics yields the Fibonacci family of dynamical universality classes which has the diffusive and Kardar-Parisi-Zhang universality classes as its first two members.