Fluctuation theorems for stochastic dynamics

Abstract

Fluctuation theorems make use of time reversal to make predictions about entropyproduction in many-body systems far from thermal equilibrium. Here we review the widevariety of distinct, but interconnected, relations that have been derived and investigatedtheoretically and experimentally. Significantly, we demonstrate, in the context ofMarkovian stochastic dynamics, how these different fluctuation theorems arise from asimple fundamental time-reversal symmetry of a certain class of observables.Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropyproduction in terms of these observables. We work with the master equationapproach, which leads to a mathematically straightforward proof and providesdirect insight into the probabilistic meaning of the quantities involved. Finally, wepoint to some experiments that elucidate the practical significance of fluctuationrelations.