  We consider fluctuations of the dissipated energy in nonlinear driven
diffusive systems subject to bulk dissipation and boundary driving. With this
aim, we extend the recently-introduced macroscopic fluctuation theory to
nonlinear driven dissipative media, starting from the fluctuating hydrodynamic
equations describing the system mesoscopic evolution. Interestingly, the action
associated to a path in mesoscopic phase-space, from which large-deviation
functions for macroscopic observables can be derived, has the same simple form
as in non-dissipative systems. This is a consequence of the quasi-elasticity of
microscopic dynamics, required in order to have a nontrivial competition
between diffusion and dissipation at the mesoscale. Euler-Lagrange equations
for the optimal density and current fields that sustain an arbitrary
dissipation fluctuation are also derived. A perturbative solution thereof shows
that the probability distribution of small fluctuations is always gaussian, as
expected from the central limit theorem. On the other hand, strong separation
from the gaussian behavior is observed for large fluctuations, with a
distribution which shows no negative branch, thus violating the
Gallavotti-Cohen fluctuation theorem as expected from the irreversibility of
the dynamics. The dissipation large-deviation function exhibits simple and
general scaling forms for weakly and strongly dissipative systems, with large
fluctuations favored in the former case but heavily supressed in the latter.
(...) [see complete abstract by downloading the paper]
