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

Transient fluctuation theorems for the currents and initial equilibrium ensembles