Cellular Automata: From Structural Principles to Transport and Correlation Methods
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910081120993280 |
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| author | Metkar, Mihir Sah, Neha Zhou, Yichen |
| author_facet | Metkar, Mihir Sah, Neha Zhou, Yichen |
| contents | Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and nonequilibrium phase transitions, transport and hydrodynamic limits, kinetic roughening, self-organized criticality, and complex spatiotemporal correlations. This survey focuses on three tightly connected themes. \emph{(i)} We present a structural view of CA as shift-commuting maps on configuration spaces, emphasizing rule complexity, reversibility, and conservation laws (including discrete continuity equations). \emph{(ii)} We organize transport in CA into ballistic, diffusive, and anomalous regimes, and connect microscopic currents to macroscopic laws through Green--Kubo formulas, scaling theory, and universality classes. \emph{(iii)} We develop correlation-based methods -- from structure factors and response formulas to computational mechanics and data-driven inference -- that diagnose regimes and enable coarse-graining. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_01278 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cellular Automata: From Structural Principles to Transport and Correlation Methods Metkar, Mihir Sah, Neha Zhou, Yichen Statistical Mechanics Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and nonequilibrium phase transitions, transport and hydrodynamic limits, kinetic roughening, self-organized criticality, and complex spatiotemporal correlations. This survey focuses on three tightly connected themes. \emph{(i)} We present a structural view of CA as shift-commuting maps on configuration spaces, emphasizing rule complexity, reversibility, and conservation laws (including discrete continuity equations). \emph{(ii)} We organize transport in CA into ballistic, diffusive, and anomalous regimes, and connect microscopic currents to macroscopic laws through Green--Kubo formulas, scaling theory, and universality classes. \emph{(iii)} We develop correlation-based methods -- from structure factors and response formulas to computational mechanics and data-driven inference -- that diagnose regimes and enable coarse-graining. |
| title | Cellular Automata: From Structural Principles to Transport and Correlation Methods |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2601.01278 |