Uphill in reaction-diffusion multi-species interacting particles systems

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 particle densities evolves as the discretized version of a system of coupled heat equations with linear reactions. We show that global uphill diffusion is inhibited, whereas local uphill is still possible. As a byproduct of our study, we identify a specific one-parameter family of such linear reaction-diffusion systems where the hydrodynamic limit behaviour can be directly achieved by means of a dual process.