Complete ergodicity in one-dimensional reversible cellular automata
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911581885956096 |
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| author | Shiraishi, Naoto Takesue, Shinji |
| author_facet | Shiraishi, Naoto Takesue, Shinji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete ergodicity in one-dimensional reversible cellular automata Shiraishi, Naoto Takesue, Shinji Cellular Automata and Lattice Gases Statistical Mechanics 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. |
| title | Complete ergodicity in one-dimensional reversible cellular automata |
| topic | Cellular Automata and Lattice Gases Statistical Mechanics |
| url | https://arxiv.org/abs/2408.06691 |