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Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton
ID Buča, Berislav (Author), ID Garrahan, Juan P. (Author), ID Prosen, Tomaž (Author), ID Vanicat, Matthieu (Author)

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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.

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 This link opens in a new window
UDC:536.9
ISSN on article:2470-0045
DOI:10.1103/PhysRevE.100.020103 This link opens in a new window
COBISS.SI-ID:3354468 This link opens in a new window
Publication date in RUL:19.09.2019
Views:1710
Downloads:936
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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 This link opens in a new window

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

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