Dynamical phase transitions in the current distribution of driven diffusive channels

We study singularities in the large deviation function of the time-averaged current of diffusive
systems connected to two reservoirs. A set of conditions for the occurrence of phase transitions,
both first and second order, are obtained by deriving Landau theories. First-order transitions occur
in the absence of a particle-hole symmetry, while second-order occur in its presence and are
associated with a symmetry breaking. The analysis is done in two distinct statistical ensembles,
shedding light on previous results. In addition, we also provide an exact solution of a model
exhibiting a second-order symmetry-breaking transition.

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