Related papers: Some inequalities on generalized entropies

Some preliminary evidence suggests the conjecture that the collective behaviour of systems having long-range interactions may be described more effectively by the Tsallis rather than by the Boltzmann/Gibbs/Shannon entropy. To this end, we…

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied…

The definition of weighted entropy allows for easy calculation of the entropy of the mixture of measures. In this paper we investigate the problem of equivalent definition of the general entropy function in weighted form. We show that under…

It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability and the axiomatic foundation.

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the…

A lower bound of the reduced relative entropy is given by the use of a variational expression. The reduced Tsallis relative entropy is defined and some results are given. In particular, the convexity of the reduced Tsallis relative entropy…

The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by the use of Hermite-Hadamard inequality. Thus, we obtain alternative bounds for the Tsallis relative operator entropy. In the process to…

This article proposes a new two-parameter generalized entropy, which can be reduced to the Tsallis and the Shannon entropy for specific values of its parameters. We develop a number of information-theoretic properties of this generalized…

We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…

We establish a unified view to the polygamy of multi-party quantum entanglement in arbitrary dimensions. Using quantum Tsallis-$q$ entropy, we provide a one-parameter class of polygamy inequalities of multi-party quantum entanglement. This…

Recently, Zou obtained the generalized results on the bounds for Tsallis relative operator entropy. In this short paper, we give precise bounds for Tsallis relative operator entropy. We also give precise bounds of relative operator entropy.

In the nonextensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem[Phys. Rev. Lett. {\bf 71}, 1291(1993)] as well as its demonstration are generalized, i.e., when a pure quantum system, whose Hilbert space…

Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory…

In this paper, we investigate the partition inequality, joint convexity, and Pinsker's inequality, for a divergence that generalizes the Tsallis Relative Entropy and Kullback-Leibler divergence. The generalized divergence is defined in…

The purpose of this note is to argue that degree of nonextensivity as given by Tsallis distribution obtained from maximum entropy principle has a different origin than nonextensivity inferred from pseudo-additive property of Tsallis…

This short note contains a list of new results concerning the R\'{e}nyi entropy, the Tsallis entropy, and the Heun functions associated with positive linear operators.

Oikonomou [Physica A 386 (2007) 119] has published a calculation which purports to show that the Tsallis and Renyi entropies can be obtained from the generalized multinomial coefficients. In this paper, we prove that the method of…

The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev's axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin's axiom in…

In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.

We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…