Phase transitions and symmetry breaking in current distributions of diffusive systems

In this talk, I address the question of whether the current distribution in an equilibrium diffusive system, coupling a pair of reservoirs, can exhibit singularities. Strikingly, even when the free energy is nonsingular, the answer is yes: the distribution can exhibit a host of dynamical phase transitions, which manifest themselves as singularities in the large deviation function of the current. Based on exact Landau theories, I describe how a particle-hole symmetry breaking leads to a continuous transition, and how a small departure from the symmetry can produce a first-order transition. These mechanisms are easily generalized to nonequilibrium diffusive transport with boundary or bulk driving. Concrete realizations of the phenomena are also discussed, both from theoretical and empirical perspectives.