Criticality in Dynamic Arrest: Correspondence between Glasses and Traffic

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.

4 pages, 4 figures

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• Finite Size Effects in the Nagel-Schreckenberg Traffic Model
• Hybrid multilane models for highway traffic
• Manifestations of the onset of chaos in condensed matter and complex systems
• A criterion for condensation in kinetically constrained one-dimensional transport models
• Evidence of Non-Equilibrium Critical Phenomena in a Simple Model of Traffic