556 research outputs found
On uniqueness theorems for Tsallis entropy and Tsallis relative entropy
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
Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization
Kullback-Leibler relative-entropy has unique properties in cases involving
distributions resulting from relative-entropy minimization. Tsallis
relative-entropy is a one parameter generalization of Kullback-Leibler
relative-entropy in the nonextensive thermostatistics. In this paper, we
present the properties of Tsallis relative-entropy minimization and present
some differences with the classical case. In the representation of such a
minimum relative-entropy distribution, we highlight the use of the q-product,
an operator that has been recently introduced to derive the mathematical
structure behind the Tsallis statistics. One of our main results is
generalization of triangle equality of relative-entropy minimization to the
nonextensive case.Comment: 15 pages, change of title, revision of triangle equalit
Characterizations of generalized entropy functions by functional equations
We shall show that a two-parameter extended entropy function is characterized
by a functional equation. As a corollary of this result, we obtain that the
Tsallis entropy function is characterized by a functional equation, which is a
different form used in \cite{ST} i.e., in Proposition \ref{prop01} in the
present paper. We also give an interpretation of the functional equation giving
the Tsallis entropy function, in the relation with two non-additive properties
Additive Entropies of degree-q and the Tsallis Entropy
The Tsallis entropy is shown to be an additive entropy of degree-q that
information scientists have been using for almost forty years. Neither is it a
unique solution to the nonadditive functional equation from which random
entropies are derived. Notions of additivity, extensivity and homogeneity are
clarified. The relation between mean code lengths in coding theory and various
expressions for average entropies is discussed.Comment: 13 page
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