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.