Uphill in reaction-diffusion multi-species interacting particles systems

TL;DR

This paper investigates multi-species reaction-diffusion particle systems with boundary-driven reservoirs, identifying conditions for hydrodynamic limits and demonstrating partial uphill diffusion phenomena in discrete systems that vanish in the continuum limit.

Contribution

It introduces a specific family of linear reaction-diffusion systems where hydrodynamic limits can be analyzed via dual processes, revealing uphill diffusion effects in lattice models.

Findings

Partial uphill diffusion occurs in the discrete lattice system.

Uphill diffusion effects disappear in the hydrodynamic limit.

A specific one-parameter family of systems is characterized.

Abstract

We study reaction-diffusion processes with multi-species of particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We consider the condition that the time evolution of the average occupation evolves as the discretized version of a system of coupled diffusive equations with linear reactions. In particular, we identify a specific one-parameter family of such linear reaction-diffusion systems where the hydrodynamic limit behaviour can be obtained by means of a dual process. We show that partial uphill diffusion is possible for the discrete particle systems on the lattice, whereas it is lost in the hydrodynamic limit.