143 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
Trace inequalities in nonextensive statistical mechanics
In this short paper, we establish a variational expression of the Tsallis
relative entropy. In addition, we derive a generalized thermodynamic inequality
and a generalized Peierls-Bogoliubov inequality. Finally we give a generalized
Golden-Thompson inequality
Unitarily invariant norm inequalities for some means
We introduce some symmetric homogeneous means, and then show unitarily
invariant norm inequalities for them, applying the method established by Hiai
and Kosaki. Our new inequalities give the tighter bounds of the logarithmic
mean than the inequalities given by Hiai and Kosaki. Some properties and norm
continuities in parameter for our means are also discussed
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
Refined Young inequalities with Specht's ratio
In this paper, we show that the -weighted arithmetic mean is greater
than the product of the -weighted geometric mean and Specht's ratio. As a
corollary, we also show that the -weighted geometric mean is greater than
the product of the -weighted harmonic mean and Specht's ratio. These
results give the improvements for the classical Young inequalities, since
Specht's ratio is generally greater than 1. In addition, we give an operator
inequality for positive operators, applying our refined Young inequality.Comment: A small mistake of calculation in page 4 was corrected. References
were updated. 7 page
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