Related papers: Some remarks on Tsallis relative operator entropy
Probability distributions defined on the half space are known to be quite different from those in the full space. Here, a nonextensive entropic treatment is presented for the half space in an analytic and self-consistent way. In this…
The paper describes various approaches to the invertibility of Toeplitz plus Hankel operators in Hardy and $l^p$-spaces, integral and difference Wiener-Hopf plus Hankel operators and generalized Toeplitz plus Hankel operators. Special…
By using the Jacobi metric of the configuration space, and assuming ergodicity, we calculate the Boltzmann entropy $S$ of a finite-dimensional system around a non-degenerate critical point of its potential energy $V$. We compare $S$ with…
Recently, the spectral geometric mean has been studied by some papers. In this paper, we firstly estimate the H\"{o}lder type inequality of the spectral geometric mean of positive invertible operators on the Hilbert space for all real order…
We give a new proof of the theorems on the maximum entropy principle in Tsallis statistics. That is, we show that the $q$-canonical distribution attains the maximum value of the Tsallis entropy, subject to the constraint on the…
We study convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and obtain in this way new trace inequalities for deformed exponentials that may be considered as generalizations of…
Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy…
The Kolmogorov-Sinai entropy in the sense of Tsallis under Bernoulli shifts was obtained by Meson and Vericat [J. Math. Phys. 37, 4480(1996)]. In this paper, we propose a revised generalized Kolmogorov-Sinai-q entropy under Markov shifts.…
The necessary conditions (NC) that reconcile canonical probability distributions obtained from the q-maximum entropy principle, subjected to both i) the additive duality of generalized statistics and ii) normal averages expectations with…
The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are…
The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On…
Motivated by a recent study of Bessel operators in connection with a refinement of Hardy's inequality involving $1/\sin^2(x)$ on the finite interval $(0,\pi)$, we now take a closer look at the underlying Bessel-type operators with more…
Let $M_1$ and $M_2$ be functions on $[0,1]$ such that $M_1(t^{1/p})$ and $M_2(t^{1/p})$ are Orlicz functions for some $p \in (0,1].$ Assume that $M_2^{-1} (1/t)/M_1^{-1} (1/t)$ is non-decreasing for $t \geq 1.$ Let $(\alpha_i)_{i=1}^\infty$…
In this article, we present a new subadditivity behavior of convex and concave functions, when applied to Hilbert space operators. For example, under suitable assumptions on the spectrum of the positive operators $A$ and $B$, we prove that…
We address an information-theoretic approach to noise and disturbance in quantum measurements. Properties of corresponding probability distributions are characterized by means of both the R\'{e}nyi and Tsallis entropies. Related…
Tsallis' 'statistical thermodynamic' formulation of the nonadditive entropy of degree-\alpha is neither correct nor self-consistent.
We discuss two families of two-parameter entropies and divergences, derived from the standard R\'enyi and Tsallis entropies and divergences. These divergences and entropies are found as divergences or entropies of escort distributions.…
Within the Tsallis thermodynamics' framework, and using scaling properties of the entropy, we derive a generalization of the Gibbs-Duhem equation. The analysis suggests a transformation of variables that allows standard thermodynamics to be…
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.
Many methods have been experimented to study decoherence in nanostructures. Tsallis, Shannon and Gaussian entropy have been used to study decoherence separately; in this paper, we compared the results of the sus-mentioned entropies in…