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Communications in Mathematical Physics

, Volume 272, Issue 1, pp 53–74 | Cite as

Continuity of Information Transport in Surjective Cellular Automata

  • Torbjørn Helvik
  • Kristian Lindgren
  • Mats G. Nordahl
Article

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.

Keywords

Local Information Cellular Automaton Cellular Automaton Shannon Entropy Information Current 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Torbjørn Helvik
    • 1
  • Kristian Lindgren
    • 2
  • Mats G. Nordahl
    • 3
  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of Physical Resource TheoryChalmers University of Technology and Göteborg UniversityGöteborgSweden
  3. 3.Department of Applied Information TechnologyChalmers University of Technology and Göteborg UniversityGöteborgSweden

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