  Boundary driven diffusive systems describe a broad range of transport
phenomena. We study large deviations of the density profile in these systems,
using numerical and analytical methods. We find that the large deviation may be
non-differentiable, a phenomenon that is unique to non-equilibrium systems, and
discuss the types of models which display such singularities.\ The structure of
these singularities is found to generically be a cusp, which can be described
by a Landau free energy or, equivalently, by catastrophe theory. Connections
with analogous results in systems with finite-dimensional phase spaces are
drawn.
