TY - JOUR
T1 - Tsallis entropy and generalized Shannon additivity
AU - Jäckle, Sonja
AU - Keller, Karsten
PY - 2017/4/26
Y1 - 2017/4/26
N2 - The Tsallis entropy given for a positive parameter a 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. © 2017 by the authors.
AB - The Tsallis entropy given for a positive parameter a 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. © 2017 by the authors.
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85029535814&origin=inward&txGid=d212bc50a3e8c4fe012c3727db7f517f
U2 - 10.3390/axioms6020014
DO - 10.3390/axioms6020014
M3 - Journal articles
SN - 2075-1680
JO - Axioms
JF - Axioms
ER -
