Abstract
We consider the fluctuations of generalized currents in stochastic Markovian dynamics. Thelarge deviations of current fluctuations are shown to obey a Gallavotti–Cohen (GC) typesymmetry in systems with a finite state space. However, this symmetry is notguaranteed to hold in systems with an infinite state space. A simple exampleof such a case is the zero-range process (ZRP). Here we discuss in more detailthe already reported (Harris et al 2006 Europhys. Lett. 75 227) breakdown of theGC symmetry in the context of the ZRP with open boundaries and we give aphysical interpretation of the phases that appear. Furthermore, the earlier analyticalresults for the single-site case are extended to cover multiple-site systems. Wealso use our exact results to test an efficient numerical algorithm of Giardinà et al (2006 Phys. Rev. Lett. 96 120603), which was developed to measure the currentlarge deviation function directly. We find that this method breaks down in somephases which we associate with the gapless spectrum of an effective Hamiltonian.
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