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In a recent paper by Grunewald et.al., a new method to study hydrodynamiclimits was developed for reversible dynamics. In this work, we generalize thismethod to a family of non-reversible dynamics. As an application, we obtainquantitative rates of convergence to the hydrodynamic limit for a weaklyasymmetric version of the Ginzburg-Landau model endowed with Kawasaki dynamics.These results also imply local Gibbs behavior, following a method introduced ina recent paper by the second author.

The two-scale approach to hydrodynamic limits for non-reversible dynamics