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On the law of entropy increase of some cellular automata on Zd

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Abstract

We consider some time-reversible cellular automata on thed-dimensional integral latticeZ d and study their time evolution properties. We show first that a Boltzmann-type entropy can be defined which is not less than its initial value for initial States which have no spatial correlation. For monotonic increase of the entropies for such initial States we need an additional condition which we call renewality. Under the renewality condition entropy is monotonic nondecreasing. We give some examples of cellular automata which satisfy the renewality condition

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Authors and Affiliations

  1. Department of Mathematics, Tsuda College, Kodaira, 187, Tokyo, Japan

    Toshio Niwa

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  1. Toshio Niwa
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Correspondence to Toshio Niwa.

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Niwa, T. On the law of entropy increase of some cellular automata on Zd . J Stat Phys 89, 801–816 (1997). https://doi.org/10.1007/BF02765545

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  • DOI: https://doi.org/10.1007/BF02765545

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