Phase diagram of two-lane driven diffusive systems

TL;DR

This paper develops a stability analysis method to derive phase diagrams for two-lane driven diffusive systems, revealing complex behaviors and establishing a connection with the extremal current principle.

Contribution

It introduces a stability analysis approach for phase diagram derivation in two-lane driven diffusive systems, linking it to the extremal current principle and exploring its limitations.

Findings

Derived phase diagrams for various coupled exclusion processes.

Established the equivalence of stability analysis and extremal current principle.

Identified classes where both methods fail.

Abstract

We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail.