On uniqueness theorems for Tsallis entropy and Tsallis relative entropy

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.Comment: this was merged by two manuscripts (arXiv:cond-mat/0410270 and arXiv:cond-mat/0410271), and will be published from IEEE TI