On the Uniqueness Theorem for Pseudo-Additive Entropies

On the Uniqueness Theorem for Pseudo-Additive Entropies

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...

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Main Authors: Petr Jizba, Jan Korbel
Format: Article
Language:English
Published: MDPI AG 2017-11-01
Series:Entropy
Subjects:
pseudo-additive entropy
entropic chain rule
conditional entropy
Darótzy’s mapping
Online Access:https://www.mdpi.com/1099-4300/19/11/605
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spelling doaj-c75c1448db3c46ffaf8b6d05ce8213462020-11-25T01:02:25ZengMDPI AGEntropy1099-43002017-11-01191160510.3390/e19110605e19110605On the Uniqueness Theorem for Pseudo-Additive EntropiesPetr Jizba0Jan Korbel1Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, Prague 115 19, Czech RepublicFaculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, Prague 115 19, Czech RepublicThe 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.https://www.mdpi.com/1099-4300/19/11/605pseudo-additive entropyentropic chain ruleconditional entropyDarótzy’s mapping
collection DOAJ
language English
format Article
sources DOAJ
author Petr Jizba
Jan Korbel
spellingShingle Petr Jizba
Jan Korbel
On the Uniqueness Theorem for Pseudo-Additive Entropies
Entropy
pseudo-additive entropy
entropic chain rule
conditional entropy
Darótzy’s mapping
author_facet Petr Jizba
Jan Korbel
author_sort Petr Jizba
title On the Uniqueness Theorem for Pseudo-Additive Entropies
title_short On the Uniqueness Theorem for Pseudo-Additive Entropies
title_full On the Uniqueness Theorem for Pseudo-Additive Entropies
title_fullStr On the Uniqueness Theorem for Pseudo-Additive Entropies
title_full_unstemmed On the Uniqueness Theorem for Pseudo-Additive Entropies
title_sort on the uniqueness theorem for pseudo-additive entropies
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2017-11-01
description 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.
topic pseudo-additive entropy
entropic chain rule
conditional entropy
Darótzy’s mapping
url https://www.mdpi.com/1099-4300/19/11/605
work_keys_str_mv AT petrjizba ontheuniquenesstheoremforpseudoadditiveentropies
AT jankorbel ontheuniquenesstheoremforpseudoadditiveentropies
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