{"title":"Complete ergodicity in one-dimensional reversible cellar automata","authors":"Naoto Shiraishi, Shinji Takesue","doi":"arxiv-2408.06691","DOIUrl":null,"url":null,"abstract":"Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA)\nare investigated. We establish all the ergodic rules in CA with 3, 4, and 5\nstates. We analytically prove the ergodicity for 12 rules in 3-state CA and\n118320 rules in 5-state CA with any ergodic and periodic boundary condition,\nand numerically confirm all the other rules non-ergodic with some boundary\ncondition. We classify ergodic rules into several patterns, which exhibit a\nvariety of ergodic structure.","PeriodicalId":501231,"journal":{"name":"arXiv - PHYS - Cellular Automata and Lattice Gases","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Cellular Automata and Lattice Gases","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.06691","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.
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