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Continuity of Information Transport in Surjective Cellular Automata

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Abstract

We introduce a local version of the Shannon entropy in order to describe information transport in spatially extended dynamical systems, and to explore to what extent information can be viewed as a local quantity. Using an appropriately defined information current, this quantity is shown to obey a local conservation law in the case of one-dimensional reversible cellular automata with arbitrary initial measures. The result is also shown to apply to one-dimensional surjective cellular automata in the case of shift-invariant measures. Bounds on the information flow are also shown.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491, Trondheim, Norway

    Torbjørn Helvik

  2. Department of Physical Resource Theory, Chalmers University of Technology and Göteborg University, SE-41296, Göteborg, Sweden

    Kristian Lindgren

  3. Department of Applied Information Technology, Chalmers University of Technology and Göteborg University, SE-41756, Göteborg, Sweden

    Mats G. Nordahl

Authors
  1. Torbjørn Helvik
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  2. Kristian Lindgren
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  3. Mats G. Nordahl
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Correspondence to Torbjørn Helvik.

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Communicated by G. Gallavotti

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Helvik, T., Lindgren, K. & Nordahl, M.G. Continuity of Information Transport in Surjective Cellular Automata. Commun. Math. Phys. 272, 53–74 (2007). https://doi.org/10.1007/s00220-007-0192-8

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  • DOI: https://doi.org/10.1007/s00220-007-0192-8

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