Continuity of Information Transport in Surjective Cellular Automata |
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| Authors: | Torbjørn Helvik Kristian Lindgren Mats G. Nordahl |
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| Affiliation: | 1.Department of Mathematical Sciences,Norwegian University of Science and Technology,Trondheim,Norway;2.Department of Physical Resource Theory,Chalmers University of Technology and G?teborg University,G?teborg,Sweden;3.Department of Applied Information Technology,Chalmers University of Technology and G?teborg University,G?teborg,Sweden |
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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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