Stefan problem for a non-ergodic facilitated exclusion process
arXiv:1912.09583 · doi:10.2140/pmp.2021.2.127
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.
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Cited by in corpus (4)
- Stationary States of the One-Dimensional Discrete-Time Facilitated Symmetric Exclusion Process
- Stationary States of the One-dimensional Facilitated Asymmetric Exclusion Process
- Hydrodynamics of a hard-core active lattice gas
- Approach to Hyperuniformity in the One-Dimensional Facilitated Exclusion Process