Hydrodynamic limit of the Kawasaki dynamics on the 1D-lattice with strong, finite-range interaction

TL;DR

This paper establishes the hydrodynamic limit for a one-dimensional Kawasaki dynamics system with strong, finite-range interactions, extending previous results to more complex interacting systems.

Contribution

It introduces a novel adaptation of a two-scale approach to derive hydrodynamic limits for strongly interacting, unbounded spin systems.

Findings

Hydrodynamic limit derived for 1D Kawasaki dynamics with strong interactions.

Extension of previous results to systems with quadratic, finite-range interactions.

Method combines two-scale approach with recent techniques for conservative systems.

Abstract

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.