Related papers: Bounds for the reduced relative entropies
The form invariance of the statement of the maximum entropy principle and the metric structure in quantum density matrix theory, when generalized to nonextensive situations, is shown here to determine the structure of the nonextensive…
We introduce the relative tail entropy to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail entropy is conserved by the principal extension.
This paper proposes that the mathematical relationship between an entropy distribution and its limit offers some new insight into system performance. This relationship is used to quantify variation among the entities of a system, where…
We formulate and solve the diffusion equation over a previously studied field $\mathcal{R}$, whose construction was motivated by the Tsallis entropy composition property. We compare this solution with the solutions of the diffusion and of…
We consider the generalized differential entropy of normalized sums of independent and identically distributed (IID) continuous random variables. We prove that the R\'{e}nyi entropy and Tsallis entropy of order $\alpha\ (\alpha>0)$ of the…
In this paper we derived a 6N dimensional non-homogeneous evolution equation of Tsallis non-equilibrium entropy; presented a formula for entropy production rate (i.e. the law of entropy increase) for Tsallis entropy only when its index q>0,…
An entanglement bound based on local measurements is introduced for multipartite pure states. It is the upper bound of the geometric measure and the relative entropy of entanglement. It is the lower bound of minimal measurement entropy. For…
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,…
When the Ricci curvature of a Riemannian manifold is not lower bounded by a constant, but lower bounded by a continuous function, we give a new characterization of this lower bound through the convexity of relative entropy on the…
In this paper, we consider the problem of estimating Tsallis entropy from a given data set. We propose four different estimators for Tsallis entropy measure based on higher-order sample spacings, and then discuss estimation of Tsallis…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw [Phys. Lett. A {\bf 198} (1995) 119] has already pointed out, the concavity of Tsallis' entropy with respect to the internal energy is not sufficient…
We revisit the cut-off prescriptions which are needed in order to specify completely the form of Tsallis' maximum entropy distributions. For values of the Tsallis entropic parameter $q>1$ we advance an alternative cut-off prescription and…
A chain rule and a subadditivity for the entropy of type $\beta$, which is one of the nonadditive entropies, were derived by Z.Dar\'oczy. In this paper, we study the further relations among Tsallis type entropies which are typical…
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.
In this paper, an estimation of lower bound of topological entropy for coupled-expanding systems associated with transition matrices in compact Hausdorff spaces is given. Estimations of upper and lower bounds of topological entropy for…
A family of nonlinear ordinary differential equations with arbitrary order is obtained by using nonextensive concepts related to the Tsallis entropy. Applications of these equations are given here. In particular, a connection between…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
We introduce the telescopic relative entropy (TRE), which is a new regularisation of the relative entropy related to smoothing, to overcome the problem that the relative entropy between pure states is either zero or infinity and therefore…