eng
episciences.org
Discrete Mathematics & Theoretical Computer Science
1365-8050
2011-01-01
DMTCS Proceedings vol. AP,...
Proceedings
10.46298/dmtcs.2968
2968
journal article
Conservation Laws and Invariant Measures in Surjective Cellular Automata
Jarkko Kari
Siamak Taati
https://orcid.org/0000-0002-6503-2754
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.
https://dmtcs.episciences.org/2968/pdf
surjective cellular automata
conservation laws
invariant measures
statistical equilibrium
[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]