  We study a class of dissipative PDE's perturbed by an unbounded kick force.
Under some natural assumptions, the restrictions of solutions to integer times
form a homogeneous Markov process. Assuming that the noise is rough with
respect to the space variables and has a non-degenerate law, we prove that the
system in question satisfies a large deviation principle in tau-topology. Under
some additional hypotheses, we establish a Gallavotti-Cohen type symmetry for
the rate function of an entropy production functional and the strict positivity
and finiteness of the mean entropy production in the stationary regime. The
latter result is applicable to PDE's with strong nonlinear dissipation.
