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Open AccessArticle

On the Uniqueness Theorem for Pseudo-Additive Entropies

by 1,*,† and 1,2,3,†
1
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, Prague 115 19, Czech Republic
2
Section for Science of Complex Systems, CeMSIIS, Medical University of Vienna, Spitalgasse 23, Vienna 1090, Austria
3
Complexity Science Hub Vienna, Josefstädterstrasse 39, Vienna 1090, Austria
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2017, 19(11), 605; https://doi.org/10.3390/e19110605
Received: 19 September 2017 / Revised: 8 November 2017 / Accepted: 10 November 2017 / Published: 12 November 2017
(This article belongs to the Special Issue Selected Papers from 14th Joint European Thermodynamics Conference)
The aim of this paper is to show that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) can be determined uniquely only when one fixes the prescription for handling conditional entropies. By using the concept of Kolmogorov–Nagumo quasi-linear means, we prove this with the help of Darótzy’s mapping theorem. Our point is further illustrated with a number of explicit examples. Other salient issues, such as connections of conditional entropies with the de Finetti–Kolmogorov theorem for escort distributions and with Landsberg’s classification of non-extensive thermodynamic systems are also briefly discussed. View Full-Text
Keywords: pseudo-additive entropy; entropic chain rule; conditional entropy; Darótzy’s mapping pseudo-additive entropy; entropic chain rule; conditional entropy; Darótzy’s mapping
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Jizba, P.; Korbel, J. On the Uniqueness Theorem for Pseudo-Additive Entropies. Entropy 2017, 19, 605.

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