Transient fluctuation theorems for the currents and initial equilibrium ensembles

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 (2007 J. Stat. Phys. 127 107 ) 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 Bulnes-Cuetara et al (2014 Phys. Rev. E 89 052119 ). 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.