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We derive for the first time in the literature a rate of convergence in thehydrodynamic limit of the Kawasaki dynamics for a one-dimensional latticesystem. We use an adaptation of the two-scale approach. The main difference tothe original two-scale approach is that the observables on the mesoscopic levelare described by a projection onto splines of second order, and not by aprojection onto piecewise constant functions. This allows us to use a morenatural definition of the mesoscopic dynamics, which yields a better rate ofconvergence than the original two-scale approach.

The quantitative hydrodynamic limit of the Kawasaki dynamics