Fluctuation theorems for stochastic dynamics

TL;DR

This paper reviews fluctuation theorems in stochastic dynamics, explaining their theoretical foundations, derivations, and experimental relevance, emphasizing the role of time-reversal symmetry and Gibbs entropy in entropy production.

Contribution

It demonstrates how various fluctuation theorems originate from a fundamental time-reversal symmetry in Markovian stochastic systems, providing a unified theoretical framework.

Findings

Derivation of fluctuation theorems from time-reversal symmetry

Microscopic definition of entropy production using Gibbs entropy

Connection of theoretical results with experimental observations

Abstract

Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived and investigated theoretically and experimentally. Significantly, we demonstrate, in the context of Markovian stochastic dynamics, how these different fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropy production in terms of these observables. We work with the master equation approach, which leads to a mathematically straightforward proof and provides direct insight into the probabilistic meaning of the quantities involved. Finally, we point to some experiments that elucidate the practical significance of fluctuation relations.