Criticality in Dynamic Arrest: Correspondence between Glasses and Traffic

TL;DR

This paper explores the analogy between glass transition phenomena and traffic jam formation, identifying a true dynamical critical point with diverging correlations in traffic flow models.

Contribution

It establishes a correspondence between glassy dynamics and traffic jams, revealing a sharp transition and critical behavior in traffic models similar to kinetically constrained glasses.

Findings

Identification of a true dynamical critical point in traffic flow

Diverging correlations analogous to thermodynamic phase transitions

Traffic jams exhibit sharp transition signatures in deterministic limit

Abstract

Dynamic arrest is a general phenomenon across a wide range of dynamic systems, but the universality of dynamic arrest phenomena remains unclear. We relate the emergence of traffic jams in a simple traffic flow model to the dynamic slow down in kinetically constrained models for glasses. In kinetically constrained models, the formation of glass becomes a true (singular) phase transition in the limit $T\to 0$. Similarly, using the Nagel-Schreckenberg model to simulate traffic flow, we show that the emergence of jammed traffic acquires the signature of a sharp transition in the deterministic limit $\pp\to 1$, corresponding to overcautious driving. We identify a true dynamical critical point marking the onset of coexistence between free flowing and jammed traffic, and demonstrate its analogy to the kinetically constrained glass models. We find diverging correlations analogous to those at a critical point of thermodynamic phase transitions.