Hydrodynamic limit for two-species exclusion processes

TL;DR

This paper proves that two-species exclusion processes on a torus converge to a nonlinear diffusion equation under diffusive scaling, including spectral gap bounds, advancing understanding of nongradient interacting particle systems.

Contribution

It establishes the hydrodynamic limit for a complex two-species exclusion model with nongradient features, and provides spectral gap estimates.

Findings

Particle density converges to a nonlinear diffusion equation.

Spectral gap bounds are established for finite-volume generators.

The model accounts for exchange, creation, and annihilation effects.

Abstract

We consider two-species exclusion processes on the d-dimensional discrete torus taking the effects of exchange, creation and annihilation into account. The model is, in general, of nongradient type. We prove that the (charged) particle density converges to the solution of a certain nonlinear diffusion equation under the diffusive rescaling in space and time. We also prove a lower bound on the spectral gap for the generator of the process confined in a finite volume.