Rule 54: exactly solvable model of nonequilibrium statistical mechanics

Buča, Berislav (author), Klobas, Katja (author), Prosen, Tomaž (author)

We review recent results on an exactly solvable model of nonequilibrium statistical mechanics, specifically the classical rule 54 reversible cellular automaton and some of its quantum extensions. We discuss the exact microscopic description of nonequilibrium dynamics as well as the equilibrium and nonequilibrium stationary states. This allows us to obtain a rigorous handle on the corresponding emergent hydrodynamic description, which is treated as well. Specifically, we focus on two different paradigms of rule 54 dynamics. Firstly, we consider a finite chain driven by stochastic boundaries, where we provide exact matrix product descriptions of the nonequilibrium steady state, most relevant decay modes, as well as the eigenvector of the tilted Markov chain yielding exact large deviations for a broad class of local and extensive observables. Secondly, we treat the explicit dynamics of macro-states on an infinite lattice and discuss exact closed form results for dynamical structure factor, multi-time-correlation functions and inhomogeneous quenches. Remarkably, these results prove that the model, despite its simplicity, behaves like a regular fluid with coexistence of ballistic (sound) and diffusive (heat) transport. Finally, we briefly discuss quantum interpretation of rule 54 dynamics and explicit results on dynamical spreading of local operators and operator entanglement.

• Language: English
• Keywords: statistical mechanics, non-equilibrium systems, cellular automata, thermalization
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2021
• Number of pages: 70 str.
• Numbering: Vol. 2021, art. no. ǂ074001
• PID: 20.500.12556/RUL-130305
• UDC: 536.9
• ISSN on article: 1742-5468
• DOI: 10.1088/1742-5468/ac096b
• COBISS.SI-ID: 76119811
• Publication date in RUL: 13.09.2021

Record is a part of a journal

• Title: Journal of statistical mechanics
• Shortened title: J. stat. mech.
• Publisher: IOP Publishing
• ISSN: 1742-5468
• COBISS.SI-ID: 21517607

Secondary language

• Language: Slovenian
• Keywords: statistična mehanika, neravnovesni sistemi, celični avtomati, termalizacija

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open Many-body Non-Equilibrium Systems
• Acronym: OMNES

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0402
• Name: Matematična fizika