A two-parameter generalization of Shannon–Khinchin axioms and the uniqueness theorem

Based on the one-parameter generalization of Shannon–Khinchin (SK) axioms presented by one of the authors, and utilizing a tree-graphical representation, we have developed for the first time a two-parameter generalization of the SK axioms in accordance with the two-parameter entropy introduced by Sh...

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Bibliographic Details
Published inPhysics letters. A Vol. 368; no. 3; pp. 199 - 205
Main Authors Wada, Tatsuaki, Suyari, Hiroki
Format Journal Article
LanguageEnglish
Published Elsevier B.V 20.08.2007
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Summary:Based on the one-parameter generalization of Shannon–Khinchin (SK) axioms presented by one of the authors, and utilizing a tree-graphical representation, we have developed for the first time a two-parameter generalization of the SK axioms in accordance with the two-parameter entropy introduced by Sharma, Taneja, and Mittal. The corresponding unique theorem is also proved. It is found that our two-parameter generalization of Shannon additivity is a natural consequence from the Leibniz product rule of the two-parameter Chakrabarti–Jagannathan difference operator.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2007.04.009