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

Buča, Berislav (author), Garrahan, Juan P. (author), Prosen, Tomaž (author), Vanicat, Matthieu (author)

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.

• Language: English
• Keywords: nonequilibrium statistical physics, cellular automata
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2019
• Number of pages: Str. 020103-1-020103-6
• Numbering: Vol. 100, iss. 2
• PID: 20.500.12556/RUL-110789
• UDC: 536.9
• ISSN on article: 2470-0045
• DOI: 10.1103/PhysRevE.100.020103
• COBISS.SI-ID: 3354468
• Publication date in RUL: 19.09.2019

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., E
• Publisher: American Physical Society
• ISSN: 2470-0045
• COBISS.SI-ID: 2048366611

Secondary language

• Language: Slovenian
• Keywords: neravnovesna statistična mehanika, celični avtomati

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open many-body non-equilibrium systems
• Acronym: OMNES