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We consider the behaviour of current fluctuations in non-equilibrium stochastic Markov-processes. These fluctuations have a generic symmetry property, which is the analogue of the Gallavotti-Cohen fluctuation relation. This relation was originally derived for deterministic systems and subsequently for stochastic dynamics with bounded state-space. However, the range of its validity is still an intriguing open question. In order to make progress in this direction, we consider the one-dimensional partially asymmetric zero-range process with open boundaries. Significantly, we find that the distribution of large current fluctuations does not satisfy the Gallavotti-Cohen symmetry and that such a breakdown can generally occur in systems with unbounded state space. We also discuss the dependence of the asymptotic current distribution on the initial state of the system. |
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