  We introduce a stochastic particle system that corresponds to the
Fokker-Planck equation with decay in the many-particles limit, and study its
large deviations. We show that the large-deviation rate functional corresponds
to an energy-dissipation functional in a Gamma-convergence sense. Moreover, we
prove that the resulting functional, which involves entropic terms and the
Wasserstein metric, is again a variational formulation for the Fokker-Planck
equation with decay.
