The hydrodynamic limit appears as a law of large numbers for rescaled density profiles of a large stochastic system. We study the large deviations from this scaling limit for a particular nongradient system, the nongradient version of the Ginzburg-Landau model.
Jeremy Quastel. "Large Deviations from a Hydrodynamic Scaling Limit for a Nongradient System." Ann. Probab. 23 (2) 724 - 742, April, 1995. https://doi.org/10.1214/aop/1176988286