Hydrodynamic scaling limits with deterministic initial configurations (Q1917205)

This paper considers the hydrodynamic scaling limits for the Ginzburg-Landau and interacting diffusion models with deterministic initial configurations, which are distributed reasonably well. To get the hydrodynamic limit the author applies the method developed by \textit{M. Z. Guo}, \textit{G. C. Papanicolaou} and \textit{S. R. S. Varadhan} [Commun. Math. Phys. 118, No. 1, 31-59 (1988; Zbl 0652.60107)]. Using the fact that the underlying system has elliptic evolution, it is shown that although the initial entropy is often infinite, after a finite amount of microscopic time the entropy growth has a proper bound while the macroscopic structure of the system remains unchanged.