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arXiv · 1408.5941

Transient fluctuation theorems for the currents and initial equilibrium ensembles

Matteo Polettini·Massimiliano Esposito
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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.

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Matteo Polettini, Massimiliano Esposito. 2014-08-25. Transient fluctuation theorems for the currents and initial equilibrium ensembles. https://doi.org/10.1088/1742-5468/2014/10/p10033

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