  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.
