Complete ergodicity in one-dimensional reversible cellular automata

[2408.06691] Complete ergodicity in one-dimensional reversible cellular automata Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Nonlinear Sciences > Cellular Automata and Lattice Gases arXiv:2408.06691 (nlin) [Submitted on 13 Aug 2024 ( v1 ), last revised 16 Aug 2024 (this version, v2)] Title: Complete ergodicity in one-dimensional reversible cellular automata Authors: Naoto Shiraishi , Shinji Takesue View a PDF of the paper titled Complete ergodicity in one-dimensional reversible cellular automata, by Naoto Shiraishi and Shinji Takesue View PDF Abstract: Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules in 5-state CA with any ergodic and periodic boundary condition, and numerically confirm all the other rules non-ergodic with some boundary condition. We classify ergodic rules into several patterns, which exhibit a variety of ergodic structure. Comments: 63 pages, 47 figures Subjects: Cellular Automata and Lattice Gases (nlin.CG) ; Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2408.06691 [nlin.CG] (or arXiv:2408.06691v2 [nlin.CG] for this version) https://doi.org/10.48550/arXiv.2408.06691 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Stat. Phys. 192, 165 (2025) Related DOI : https://doi.org/10.1007/s10955-025-03529-3 Focus to learn more DOI(s) linking to related resources Submission history From: Naoto Shiraishi [ view email ] [v1] Tue, 13 Aug 2024 07:29:32 UTC (2,464 KB) [v2] Fri, 16 Aug 2024 02:02:22 UTC (2,464 KB) Full-text links: Access Paper: View a PDF of the paper titled Complete ergodicity in one-dimensional reversible cellular automata, by Naoto Shiraishi and Shinji Takesue View PDF view license Current browse context: nlin.CG < prev | next > new | recent | 2024-08 Change to browse by: cond-mat cond-mat.stat-mech nlin References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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