Non-differentiable large-deviation functionals in boundary-driven diffusive systems

We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy in non-equilibrium systems. These singularities are unique to non-equilibrium systems and are a direct consequence of the breaking of time-reversal symmetry. The singular behavior is shown in an exactly solvable model and also in numerical simulations on a boundary-driven Ising model. We argue that this is expected to occur in models where the compressibility has a deep minimum. The mechanism is explained using a simple model.