Entrainment and unit velocity: Surprises in an accelerated exclusion process

TL;DR

This paper studies an accelerated exclusion process with distance-dependent interactions, revealing a sharp transition to a phase where holes form a train moving at unit velocity, with implications for understanding collective dynamics.

Contribution

It introduces a novel class of interactions in AEP inspired by RNA polymerase behavior, uncovering a discontinuous phase transition and a unique hole-train phenomenon.

Findings

Discontinuous transition from homogeneous to phase-segregated state.

Holes form a loosely bound train moving at unit velocity.

Current-density relation is J=1−ρ, indicating constant hole-train speed.

Abstract

We introduce a class of distance-dependent interactions in an accelerated exclusion process (AEP) inspired by the observation of transcribing RNA polymerase speeding up when "pushed" by a trailing one. On a ring, the AEP steady state displays a discontinuous transition, from being homogeneous (with augmented currents) to phase-segregated. In the latter state, the holes appear loosely bound and move together, much like a train. Surprisingly, the current-density relation is simply $J=1-\rho$, signifying that the "hole-train" travels with \textit{unit} velocity.