EXTENDED ENTROPIES AND DISORDER

Matt Davison () and J. S. Shiner ()
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Matt Davison: Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada
J. S. Shiner: The Shiner Group, Bergacher 3, CH-3325 Hettiswil, Switzerland;

Advances in Complex Systems (ACS), 2005, vol. 08, issue 01, 125-158

Abstract: Landsberg's notion of disorder, entropy normalized to maximum entropy, was originally proposed for the Shannon information-theoretic entropy to overcome extensivity-based deficiencies of entropy as a measure of disorder. We generalize Landsberg's concept to three classes of extended entropies: Rényi, Tsallis and Landsberg–Vedral. We show an intimate connection between the Rényi disorders and the spectrum of dimensions known as multifractals. Three examples are treated, including one for power law distributions and one based on the logistic map. On the basis of the three examples, it is demonstrated that all three classes of extended disorder are required to fully characterize the corresponding properties of a system. We conjecture, and sketch a proof to support, that all three extended disorders are also sufficient to completely determine a dimension spectrum.

Keywords: Entropy; Landsberg disorder; Rényi entropy; Tsallis entropy; multifractals; nonlinear dynamics; power law distributions; discrete logistic map (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:acsxxx:v:08:y:2005:i:01:n:s0219525905000373

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DOI: 10.1142/S0219525905000373

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