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

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.

Keywords

neravnovesna statistična mehanika;celični avtomati;nonequilibrium statistical physics;cellular automata;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 536.9
COBISS: 3354468 Link will open in a new window
ISSN: 2470-0045
Views: 657
Downloads: 706
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: Slovenian
Secondary keywords: neravnovesna statistična mehanika;celični avtomati;
Pages: str. 020103-1-020103-6
Volume: ǂVol. ǂ100
Issue: ǂiss. ǂ2
Chronology: 2019
DOI: 10.1103/PhysRevE.100.020103
ID: 11228384