The talk will present recent progress in understanding singularities in the density large deviation functional in non-equilibrium systems. First, a general overview of the methods for carrying out such calculations will be outlined. Then the analytical structure of the large deviation functionals, will be contrasted with that of equilibrium systems. Particular emphasis will be placed on cases where the functional become singular and how the singularities can be characterized. Time permitting a Casimir effect in diffusive systems will also be discussed.

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