Fluctuation theorems for stochastic interacting particle systems
2014, v.20, №1, 3-44
Fluctuation theorems such as the Gallavotti - Cohen theorem or the Jarzynski relation make use of time reversal to establish a symmetry property of the large deviation function and make predictions about entropy production in many-body systems with non-reversible dynamics. We demonstrate, in the context of Markovian jump processes with finite state space, how a wide variety of related fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. We also point out that a specific example of these fluctuation relations, which we call the Gallavotti - Cohen symmetry, may fail if the state space becomes infinite. We work with the master equation approach, which leads to mathematically straightforward proofs and provides direct insight into the probabilistic meaning of the quantities involved.
Keywords: fluctuation theorems,entropy production,time reversal,large deviations