  We consider the behaviour of current fluctuations in 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.

Statistical Mechanics