A Variational Structure for Interacting Particle Systems and their Hydrodynamic Scaling Limits

TL;DR

This paper develops a variational framework for reversible interacting particle systems, analyzing their microscopic action functionals and establishing conditions for convergence to macroscopic fluctuation action functionals in hydrodynamic limits.

Contribution

It introduces a non-quadratic microscopic action functional and proves its convergence to the quadratic macroscopic functional, advancing the understanding of hydrodynamic limits.

Findings

Convergence of microscopic action to macroscopic fluctuation functional

Applicability to symmetric simple exclusion and zero-range processes

Provides a rigorous basis for hydrodynamic limit analysis

Abstract

We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional for these systems. We analyse the behaviour of this functional in the hydrodynamic limit and we establish conditions under which it converges to the (quadratic) action functional of Macroscopic Fluctuation Theory. We discuss the implications of these results for rigorous analysis of hydrodynamic limits.