Next Article in Journal
Scalable and Fully Distributed Localization in Large-Scale Sensor Networks
Previous Article in Journal
No Uncountable Polish Group Can be a Right-Angled Artin Group
Article Menu

Export Article

Open AccessArticle

Tsallis Entropy and Generalized Shannon Additivity

Institute of Mathematics, University of Lübeck, D-23562 Lübeck, Germany
Author to whom correspondence should be addressed.
Academic Editor: Abbe Mowshowitz
Axioms 2017, 6(2), 14;
Received: 19 May 2017 / Revised: 8 June 2017 / Accepted: 10 June 2017 / Published: 14 June 2017
PDF [226 KB, uploaded 14 June 2017]


The Tsallis entropy given for a positive parameter α can be considered as a generalization of the classical Shannon entropy. For the latter, corresponding to α = 1 , there exist many axiomatic characterizations. One of them based on the well-known Khinchin-Shannon axioms has been simplified several times and adapted to Tsallis entropy, where the axiom of (generalized) Shannon additivity is playing a central role. The main aim of this paper is to discuss this axiom in the context of Tsallis entropy. We show that it is sufficient for characterizing Tsallis entropy, with the exceptions of cases α = 1 , 2 discussed separately. View Full-Text
Keywords: Tsallis entropy; Shannon entropy; additivity; axiomatics Tsallis entropy; Shannon entropy; additivity; axiomatics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Jäckle, S.; Keller, K. Tsallis Entropy and Generalized Shannon Additivity. Axioms 2017, 6, 14.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top