SciPost Submission Page
Ergodic behaviors in reversible 3-state cellular automata
by Rustem Sharipov, Matija Koterle, Sašo Grozdanov, Tomaž Prosen
Submission summary
| Authors (as registered SciPost users): | Rustem Sharipov |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2503.16593v2 (pdf) |
| Data repository: | https://zenodo.org/records/17117722 |
| Date submitted: | Oct. 31, 2025, 2:55 p.m. |
| Submitted by: | Rustem Sharipov |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
AI tools were used for grammar editing.
Abstract
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of ergodic behavior, we perform a systematic study of three-state cellular automata (with a stable `vacuum' state and `particles' with $\pm$ charges). The classification is aided by the automata's different transformation properties under discrete symmetries: charge conjugation, spatial parity and time reversal. In particular, we propose a simple classification that distinguishes between types and levels of ergodic behavior in such system as quantified by the following observables: the mean return time, the number of conserved quantities, and the scaling of correlation functions. In each of the physically distinct classes, we present examples and discuss some of their phenomenology. This includes chaotic or ergodic dynamics, phase-space fragmentation, Ruelle-Pollicott resonances, existence of quasilocal charges, and anomalous transport with a variety of dynamical exponents.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
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- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block