Stefan problem for a nonergodic facilitated exclusion process

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