Invariant measures of exclusion processes with a look-ahead rule

TL;DR

This paper analyzes a one-dimensional exclusion process with a look-ahead rule, identifying conditions for explicit invariant measures and deriving a stationary current that accounts for correlations.

Contribution

It characterizes rates with explicit Ising-Gibbs invariant measures and derives a closed-form stationary current including correlation effects.

Findings

Identifies rates with explicit invariant measures governed by pairwise balance.

Derives a stationary current matching mean-field predictions for uncorrelated particles.

Quantifies correlation-induced corrections for non-trivial interactions.

Abstract

We study a one-dimensional exclusion process with a fixed jump length $I \ge 1$ in which a particle may advance or retreat $I$ sites provided all intermediate sites are vacant, with hopping rates of Arrhenius type depending on the local headway. We identify the class of rates admitting an explicit Ising-Gibbs invariant measure, with stationarity governed by pairwise balance rather than detailed balance. In the thermodynamic limit, we derive a closed-form stationary current that recovers the mean-field prediction for look-ahead traffic flow models exactly when particles are uncorrelated, and quantifies the correlation-induced correction for non-trivial interactions, illustrated with two explicit families of interaction potentials.