Quasi-static hydrodynamic limits

TL;DR

This paper rigorously analyzes the quasi-static hydrodynamic limits of interacting particle systems with open boundaries, extending results from symmetric simple exclusion to zero range models and anharmonic oscillators with temperature gradients.

Contribution

It introduces a rigorous framework for quasi-static limits in non-equilibrium systems, using duality and entropy methods to handle various models and boundary conditions.

Findings

Hydrodynamic profiles evolve quasi-statically under slow boundary parameter changes.

Duality simplifies analysis for symmetric simple exclusion systems.

Entropy methods extend results to zero range and oscillator models.

Abstract

We consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve quasi-statically. These limits define rigorously the thermodynamic quasi static transformations also for transition between non-equilibrium stationary states. We study first the case of the symmetric simple exclusion, where duality can be used, and then we use relative entropy methods to extend to other models like zero range systems. Finally we consider a chain of anharmonic oscillators in contact with a thermal Langevin bath with a temperature gradient and a slowly varying tension applied to one end.