Complete ergodicity in one-dimensional reversible cellular automata
Cellular Automata and Lattice Gases
2026-04-13 v2 Statistical Mechanics
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.
Keywords
Cite
@article{arxiv.2408.06691,
title = {Complete ergodicity in one-dimensional reversible cellular automata},
author = {Naoto Shiraishi and Shinji Takesue},
journal= {arXiv preprint arXiv:2408.06691},
year = {2026}
}
Comments
63 pages, 47 figures