相关论文: Entropies and the derivatives of some Heun functio…
This article is a continuation of my paper [arxiv: 1409.1015v2]. R\'enyi and Tsallis entropies are associated to positive linear operators and properties of some functions related to these entropies are investigated.
We consider the indices of coincidence for the binomial, Poisson, and negative binomial distributions. They are related in a simple manner to the R\'{e}nyi entropy and Tsallis entropy. We investigate some families of Heun functions…
The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we present the regular solution of these equations, as well.…
Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon,…
We give the tight bounds of Tsallis relative operator entropy by using Hermite-Hadamard's inequality. Some reverse inequalities related to Young inequalities are also given. In addition, operator inequalities for normalized positive linear…
We consider a family of probability distributions depending on a real parameter and including the binomial, Poisson and negative binomial distributions. The corresponding index of coincidence satisfies a Heun differential equation and is a…
We establish a reverse inequality for Tsallis relative operator entropy involving a positive linear map. In addition, we present converse of Ando's inequality, for each parameter. We give examples to compare our results with the known…
The present article reveals important properties of the confluent Heun's functions. We derive a set of novel relations for confluent Heun's functions and their derivatives of arbitrary order. Specific new subclasses of confluent Heun's…
We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
Let $A$ and $B$ be two accretive operators. We first introduce the weighted geometric mean of $A$ and $B$ together with some related properties. Afterwards, we define the relative entropy as well as the Tsallis entropy of $A$ and $B$. The…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
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.
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…
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…
In this paper we study certain properties of R\'{e}nyi entropy functionals $H_\alpha(\mathcal{P})$ on the space of probability distributions over $\mathbb{Z}_+$. Primarily, continuity and convergence issues are addressed. Some properties…
In this paper a new operational definition of Renyi entropy and Renyi divergence is presented. Other operational definitions are mentioned.
We prove characterization theorems for relative entropy (also known as Kullback-Leibler divergence), q-logarithmic entropy (also known as Tsallis entropy), and q-logarithmic relative entropy. All three have been characterized axiomatically…
Uncertainty relations emerging from the Tsallis entropy are derived and discussed. In particular we found a positively defined function that saturates the so called entropic inequalities for entropies characterizing the physical states…
We analyze systematically composable composite entropy of two Tsallis subsystems with different q indices. H-theorem and thermal balance relation are commented.