Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton

Buča, Berislav; Garrahan, Juan P.; Prosen, Tomaž; Vanicat, Matthieu

Abstract

We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the Fredrickson-Andersen kinetically constrained model (KCM). By means of a matrix product ansatz, we compute the exact large deviation cumulant generating functions for a wide range of time-extensive observables of the dynamics, together with their associated rate functions and conditioned long-time distributions over configurations. We show that for all instances of boundary driving the CA dynamics occurs at the point of phase coexistence between competing active and inactive dynamical phases, similar to what happens in more standard KCMs. We also find the exact finite size scaling behavior of these trajectory transitions, and provide the explicit “Doob-transformed” dynamics that optimally realizes rare dynamical events.

Citation

Buča, B., Garrahan, J. P., Prosen, T., & Vanicat, M. (2019). Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton. Physical Review E, 100(2), 1-6. https://doi.org/10.1103/physreve.100.020103

• Journal Article Type: Article
• Acceptance Date: Jul 24, 2019
• Online Publication Date: Aug 19, 2019
• Publication Date: Aug 19, 2019
• Deposit Date: Sep 23, 2019
• Publicly Available Date: Sep 23, 2019
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 100
• Issue: 2
• Article Number: 020103(R)
• Pages: 1-6
• DOI: https://doi.org/10.1103/physreve.100.020103
• Public URL: https://nottingham-repository.worktribe.com/output/2648490
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.020103
• Contract Date: Sep 23, 2019