Statistical Equilibrium in Deterministic Cellular Automata

  • Siamak TaatiEmail author
Part of the Emergence, Complexity and Computation book series (ECC, volume 27)


Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal disorder. This chapter is an exposition of this phenomenon and of a statistical scheme for its explanation. The formulation is in the same vein as Boltzmann’s ideas, but the simple combinatorial set-up offers clarification and hope for generic mathematically rigorous results. Probabilities represent frequencies and subjective interpretations are avoided.



Research supported by ERC Advanced Grant 267356-VARIS of Frank den Hollander. I would like to thank Aernout van Enter, Nazim Fatès and Ville Salo for helpful comments and discussions. This article is dedicated with love and appreciation to my teacher Javaad Mesgari.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.University of British ColumbiaVancouverCanada

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