Transient fluctuation theorems for the currents and initial equilibrium ensembles

TL;DR

This paper proves a transient fluctuation theorem for currents in Markov jump processes, extending previous asymptotic results to finite times, and introduces a method to eliminate initial ensemble effects using a suitable equilibrium state.

Contribution

It generalizes an asymptotic fluctuation theorem to finite times and provides a graph theoretical framework for transient regimes in Markov processes.

Findings

Derived a finite-time fluctuation theorem for Markov jump processes.

Introduced a graph decomposition into cycle and tidal currents.

Applied the theory to a chemical engine model.

Abstract

We prove a transient fluctuation theorem for the currents for continuous-time Markov jump processes with stationary rates, generalizing an asymptotic result by Andrieux and Gaspard [J. Stat. Phys. 127, 107 (2007)] to finite times. The result is based on a graph theoretical decomposition in cycle currents and an additional set of tidal currents that characterize the transient relaxation regime. The tidal term can then be removed by a preferred choice of a suitable initial equilibrium ensemble, a result that provides the general theory for the fluctuation theorem without ensemble quantities recently addressed in [Phys. Rev. E 89, 052119 (2014)]. As an example we study the reaction network of a simple stochastic chemical engine, and finally we digress on general properties of fluctuation relations for more complex chemical reaction networks.