Steady-state selection in multi-species driven diffusive systems

¹ Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), CY Cergy Paris Université 95302 Cergy-Pontoise, France
² Departamento de Matemática, Instituto Superior Técnico - Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Received: 13 October 2023
Accepted: 6 March 2024

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.