On uniqueness theorems for Tsallis entropy and Tsallis relative entropy
Shigeru Furuichi
TL;DR
This paper generalizes and simplifies the uniqueness theorems for Tsallis entropy and Tsallis relative entropy using generalized axioms, providing a clearer theoretical foundation for these entropy measures.
Contribution
It introduces generalized axioms to unify and streamline the proofs of uniqueness theorems for Tsallis entropy and relative entropy.
Findings
Unified axiomatic framework for Tsallis entropy and relative entropy
Simplified proofs of their uniqueness theorems
Extended theorems to broader classes of entropy measures
Abstract
The uniqueness theorem for Tsallis entropy was presented in {\it H.Suyari, IEEE Trans. Inform. Theory, Vol.50, pp.1783-1787 (2004)} by introducing the generalized Shannon-Khinchin's axiom. In the present paper, this result is generalized and simplified as follows: {\it Generalization}: The uniqueness theorem for Tsallis relative entropy is shown by means of the generalized Hobson's axiom. {\it Simplification}: The uniqueness theorem for Tsallis entropy is shown by means of the generalized Faddeev's axiom.
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