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Moving Frames of Reference, Relativity and Invariance in Transfer Entropy and Information Dynamics

by Joseph T. Lizier 1,2,3,* and John R. Mahoney 4,5,*
1
CSIRO Information and Communications Technology Centre, PO Box 76, Epping, NSW 1710, Australia
2
School of Information Technologies, The University of Sydney, NSW 2006, Australia
3
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D-04103 Leipzig, Germany
4
Physics Department, University of California, Davis, CA 95616, USA
5
School of Natural Sciences, University of California, Merced, CA 95344, USA
*
Authors to whom correspondence should be addressed.
Entropy 2013, 15(1), 177-197; https://doi.org/10.3390/e15010177
Received: 16 November 2012 / Accepted: 31 December 2012 / Published: 10 January 2013
(This article belongs to the Special Issue Transfer Entropy)
We present a new interpretation of a local framework for informationdynamics, including the transfer entropy, by defining a moving frame of reference for theobserver of dynamics in lattice systems. This formulation is inspired by the idea ofinvestigating “relativistic” effects on observing the dynamics of information - in particular,we investigate a Galilean transformation of the lattice system data. In applying thisinterpretation to elementary cellular automata, we demonstrate that using a moving frameof reference certainly alters the observed spatiotemporal measurements of informationdynamics, yet still returns meaningful results in this context. We find that, as expected,an observer will report coherent spatiotemporal structures that are moving in their frame asinformation transfer, and structures that are stationary in their frame as information storage.Crucially, the extent to which the shifted frame of reference alters the results dependson whether the shift of frame retains, adds or removes relevant information regarding thesource-destination interaction. View Full-Text
Keywords: information theory; information transfer; information storage; transfer entropy; information dynamics; cellular automata; complex systems information theory; information transfer; information storage; transfer entropy; information dynamics; cellular automata; complex systems
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Lizier, J.T.; Mahoney, J.R. Moving Frames of Reference, Relativity and Invariance in Transfer Entropy and Information Dynamics. Entropy 2013, 15, 177-197.

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