On the Two Species Asymmetric Exclusion Process with Semi-Permeable Boundaries

Abstract

We investigate the structure of the nonequilibrium stationary state (NESS) of a system of first and second class particles, as well as vacancies (holes), on L sites of a one-dimensional lattice in contact with first class particle reservoirs at the boundary sites; these particles can enter at site 1, when it is vacant, with rate alpha, and exit from site L with rate beta. Second class particles can neither enter nor leave the system, so the boundaries are semi-permeable. The internal dynamics are described by the usual totally asymmetric exclusion process (TASEP) with second class particles. An exact solution of the NESS was found by Arita. Here we describe two consequences of the fact that the flux of second class particles is zero. First, there exist (pinned and unpinned) fat shocks which determine the general structure of the phase diagram and of the local measures; the latter describe the microscopic structure of the system at different macroscopic points (in the limit L going to infinity in terms of superpositions of extremal measures of the infinite system. Second, the distribution of second class particles is given by an equilibrium ensemble in fixed volume, or equivalently but more simply by a pressure ensemble, in which the pair potential between neighboring particles grows logarithmically with distance. We also point out an unexpected feature in the microscopic structure of the NESS for finite L: if there are n second class particles in the system then the distribution of first class particles (respectively holes) on the first (respectively last) n sites is exchangeable.

28 pages, 4 figures. Changed title and introduction for clarity, added references

References in corpus (4)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Stochastic interacting particle systems out of equilibrium
• Two-Species Asymmetric Simple Exclusion Process with Open Boundaries
• Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process

Cited by in corpus (25)

• Some Exact Results for the Exclusion Process
• Matrix product formula for Macdonald polynomials
• Open two-species exclusion processes with integrable boundaries
• Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
• Combinatorics of the two-species ASEP and Koornwinder moments
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• TASEP on a ring with internal degrees of freedom
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• The exact phase diagram for a class of multispecies asymmetric exclusion processes
• Combinatorial mappings of exclusion processes
• Matrix product solution to multi-species ASEP with open boundaries
• Tableaux combinatorics of the two-species PASEP
• On Some Classes of Open Two-Species Exclusion Processes
• Renyi entropy of the totally asymmetric exclusion process
• Matrix product solution of a left-permeable two-species asymmetric exclusion process
• Matrix ansatz and combinatorics of the $k$-species PASEP
• Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring
• Dependence of the transportation time on the sequence in which particles with different hopping probabilities enter a lattice
• Domain wall of the totally asymmetric exclusion process without particle number conservation
• The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps
• The phase diagram for a multispecies left-permeable asymmetric exclusion process
• The phase diagram for a class of multispecies permissive asymmetric exclusion processes
• Synchronized shocks in an inhomogeneous exclusion process
• TASEP and Planar Binary Trees: A Combinatorial Approach
• Limiting directions for random walks in classical affine Weyl groups