We derive a large deviation principle for the empirical currents of lattice gas dynamics which combine a fast stirring mechanism (Symmetric Simple Exclusion Process) and creation/annihilation mechanisms (Glauber dynamics). Previous results on the density large deviations can be recovered from this general large deviation principle. The contribution of external driving forces due to reservoirs at the boundary of the system is also taken into account.
Thierry Bodineau. Maxime Lagouge. "Large deviations of the empirical currents for a boundary-driven reaction diffusion model." Ann. Appl. Probab. 22 (6) 2282 - 2319, December 2012. https://doi.org/10.1214/11-AAP826