Hydrodynamics of Multi-Species Driven Diffusive Systems with Open Boundaries: A Two-Tasep Study

Abstract: In this short note, we review a recently developed method for analysing multi-component driven diffusive systems with open boundaries. The approach generalises the extremal-current principle known for single-component models and is based on solving the Riemann problem for the corresponding hydrodynamic equations. As a case study, we focus on a two-species exclusion process on a lattice (Two-TASEP), where two types of particles move in opposite directions with two arbitrary rates and exchange positions upon encounter with a third rate. Despite its simplicity, this toy model effectively captures the key features of multi-species driven diffusive systems, including phase separation phenomena. This allows us to illustrate the critical role played by the underlying Riemann invariants in determining the system's macroscopic behavior.