Steady-state selection in multi-species driven diffusive systems

TL;DR

This paper presents a new method for analyzing the steady-state behavior of multi-species driven diffusive systems, extending existing principles and emphasizing the role of system-wide dynamics and Riemann variables.

Contribution

It introduces a general approach based on solving Riemann problems to determine steady states in multi-species systems, generalizing the max-min current principle.

Findings

The method accurately predicts phase diagrams of multi-species systems.

Effective reservoir densities depend on both boundary rates and overall system dynamics.

Theoretical predictions match numerical simulations across models.

Abstract

We introduce a general method to determine the large scale non-equilibrium steady-state properties of one-dimensional multi-species driven diffusive systems with open boundaries, generalizing thus the max-min current principle known for systems with a single type of particles. This method is based on the solution of the Riemann problem of the associated system of conservation laws. We demonstrate that the effective density of a reservoir depends not only on the corresponding boundary hopping rates but also on the dynamics of the entire system, emphasizing the interplay between bulk and reservoirs. We highlight the role of Riemann variables in establishing the phase diagram of such systems. We apply our method to three models of multi-species interacting particle systems and compare the theoretical predictions with numerical simulations.