Tsallis Entropy and Generalized Shannon Additivity
Institute of Mathematics, University of Lübeck, D-23562 Lübeck, Germany
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Academic Editor: Abbe Mowshowitz
Axioms 2017, 6(2), 14; https://doi.org/10.3390/axioms6020014
Received: 19 May 2017 / Revised: 8 June 2017 / Accepted: 10 June 2017 / Published: 14 June 2017
The Tsallis entropy given for a positive parameter can be considered as a generalization of the classical Shannon entropy. For the latter, corresponding to , 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 discussed separately.
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Keywords:
Tsallis entropy; Shannon entropy; additivity; axiomatics
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MDPI and ACS Style
Jäckle, S.; Keller, K. Tsallis Entropy and Generalized Shannon Additivity. Axioms 2017, 6, 14. https://doi.org/10.3390/axioms6020014
AMA Style
Jäckle S, Keller K. Tsallis Entropy and Generalized Shannon Additivity. Axioms. 2017; 6(2):14. https://doi.org/10.3390/axioms6020014
Chicago/Turabian StyleJäckle, Sonja; Keller, Karsten. 2017. "Tsallis Entropy and Generalized Shannon Additivity" Axioms 6, no. 2: 14. https://doi.org/10.3390/axioms6020014
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