Stefan problem for a non-ergodic facilitated exclusion process

TL;DR

This paper studies a non-ergodic, kinetically constrained exclusion process and shows that its large-scale behavior is described by a free boundary problem, linking microscopic phases to macroscopic interface dynamics.

Contribution

It establishes the hydrodynamic limit of the facilitated exclusion process as a free boundary problem, connecting microscopic phase separation to macroscopic interface evolution.

Findings

Hydrodynamic limit governed by a free boundary problem.

Microscopic blocked/ergodic phases correspond to macroscopic interfaces.

Degenerate jump rates lead to phase separation and phase transitions.

Abstract

We consider the facilitated exclusion process, which is a nonergodic, kinetically constrained exclusion process. We show that in the hydrodynamic limit, its macroscopic behavior is governed by a free boundary problem. The particles evolve on the one-dimensional lattice according to jump rates which are degenerate, since they can vanish on non-trivial configurations and create distinct phases: indeed, configurations can be totally blocked (they cannot evolve under the dynamics), ergodic (they belong to an irreducible component), or transient (after a transitive period of time they will become either blocked or ergodic). We additionally prove that the microscopic separation into blocked/ergodic phases fully coincides with the moving interface problem given by the hydrodynamic equation.