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  1. Home > Articles & Issues >
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  3. Conservation Laws an ...
Conference paper

Conservation Laws and Invariant Measures in Surjective Cellular Automata

Jarkko Kari ORCID (1) (2), Siamak Taati ORCID (3)
(1) Departement of Mathematics, University of Turku
(2) University of Turku
(3) Department of Mathematics
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Imported on
January 31, 2017
Published on
December 31, 2010
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AP, Automata 2011 - 17th International Workshop on Cellular Automata and Discrete Complex Systems
Proceedings
DOI
10.46298/dmtcs.2968
License
https://about.hal.science/hal-authorisation-v1
Research Council of Finland
131558
Cellular automata and discrete dynamical systems
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709
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Conservation Laws and Invariant Measures in Surjective Cellular Automata

Jarkko Kari ORCID (1) (2), Siamak Taati ORCID (3)
(1) Departement of Mathematics, University of Turku
(2) University of Turku
(3) Department of Mathematics
Abstract
We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of one-dimensional surjective cellular automata. We also discuss a generalization of this fact to Markov measures and higher-range conservation laws in arbitrary dimension. As a corollary, we show that the uniform Bernoulli measure is the only shift-invariant, full-support Markov measure that is invariant under a strongly transitive cellular automaton.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
  • [NLIN.NLIN-CG]Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • surjective cellular automata
  • conservation laws
  • invariant measures
  • statistical equilibrium
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