The asymmetric simple exclusion process with an open boundary

TL;DR

This paper analyzes the asymmetric simple exclusion process with an open boundary, deriving formulas for transition probabilities over time, which enhances understanding of particle dynamics in confined systems with boundary interactions.

Contribution

It provides explicit formulas for transition probabilities in the ASEP with an open boundary, a novel analytical result for this class of stochastic processes.

Findings

Derived explicit transition probability formulas

Enhanced understanding of boundary-driven particle systems

Applicable to non-equilibrium statistical mechanics

Abstract

We consider the asymmetric simple exclusion process confined to the nonnegative integers with an open boundary at 0. The point 0 is connected to a reservoir where particles are injected and ejected at prescribed rates subject to the exclusion rule. We derive formulas for the transition probability as a function of time from states where initially there are m particles to states where there are n particles.