Information Shift Dynamics Described by Tsallis q = 3 Entropy on a Compact Phase Space |
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Authors: | Jin Yan Christian Beck |
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Affiliation: | 1.Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany;2.School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK;3.The Alan Turing Institute, London NW1 2DB, UK |
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Abstract: | Recent mathematical investigations have shown that under very general conditions, exponential mixing implies the Bernoulli property. As a concrete example of statistical mechanics that are exponentially mixing we consider the Bernoulli shift dynamics by Chebyshev maps of arbitrary order , which maximizes Tsallis entropy rather than the ordinary Boltzmann-Gibbs entropy. Such an information shift dynamics may be relevant in a pre-universe before ordinary space-time is created. We discuss symmetry properties of the coupled Chebyshev systems, which are different for even and odd N. We show that the value of the fine structure constant is distinguished as a coupling constant in this context, leading to uncorrelated behaviour in the spatial direction of the corresponding coupled map lattice for . |
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Keywords: | information shift Tsallis entropy Chebyshev maps fine structure constant |
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