  We derive the hydrodynamic limit of the Kawasaki dynamics for the
one-dimensional conservative system of unbounded real-valued spins with
arbitrary strong, quadratic and finite-range interactions. This extends prior
results for non-interacting spin systems. The result is obtained by adapting
two scale approach of Grunewald, Otto, Villani and Westdickenberg combined with
the authors' recent approach on conservative systems with strong interactions.

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