The two-scale approach to hydrodynamic limits for non-reversible   dynamics
  In a recent paper by Grunewald et.al., a new method to study hydrodynamic limits was developed for reversible dynamics. In this work, we generalize this method to a family of non-reversible dynamics. As an application, we obtain quantitative rates of convergence to the hydrodynamic limit for a weakly asymmetric version of the Ginzburg-Landau model endowed with Kawasaki dynamics. These results also imply local Gibbs behavior, following a method introduced in a recent paper by the second author. 
Manh Hong Duong and Max Fathi
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