Hierarchy of boundary driven phase transitions in multi-species particle systems

TL;DR

This paper classifies and analyzes boundary-driven phase transitions in multi-species particle systems, revealing kinetic mechanisms and paths for controlling system states, with validation through simulations and applicable to various driven diffusive systems.

Contribution

It introduces a framework for classifying boundary-driven phase transitions and constructs minimal paths to observe and control these transitions in multi-species systems.

Findings

Identification of kinetic mechanisms governing phase transitions.

Construction of minimal paths for state control.

Validation through numerical and Monte Carlo simulations.

Abstract

Interacting systems with $K$ driven particle species on a open chain or chains which are coupled at the ends to boundary reservoirs with fixed particle densities are considered. We classify discontinuous and continuous phase transitions which are driven by adiabatic change of boundary conditions. We build minimal paths along which any given boundary driven phase transition (BDPT) is observed and reveal kinetic mechanisms governing these transitions. Combining minimal paths, we can drive the system from a stationary state with all positive characteristic speeds to a state with all negative characteristic speeds, by means of adiabatic changes of the boundary conditions. We show that along such composite paths one generically encounters $Z$ discontinuous and $2(K-Z)$ continuous BDPTs with $Z$ taking values $0\leq Z\leq K$ depending on the path. As model examples we consider solvable exclusion processes with product measure states and $K=1,2,3$ particle species and a non-solvable two-way traffic model. Our findings are confirmed by numerical integration of hydrodynamic limit equations and by Monte Carlo simulations. Results extend straightforwardly to a wide class of driven diffusive systems with several conserved particle species.