Related papers: Relative Entropy and Tsallis Entropy of two Accret…

Functional version for the so-called Furuta parametric relative operator entropy is here investigated. Some related functional inequalities are also discussed. The theoretical results obtained by our functional approach immediately imply…

Tsallis and R\'{e}nyi entropy measures are two possible different generalizations of the Boltzmann-Gibbs entropy (or Shannon's information) but are not generalizations of each others. It is however the Sharma-Mittal measure, which was…

We show that Abe's general pseudoadditivity for entropy prescribed by thermal equilibrium in nonextensive systems holds not only for entropy, but also for energy. The application of this general pseudoadditivity to Tsallis entropy tells us…

Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…

Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…

Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in…

We show that Tsallis ensemble of power-law distributions provides a mechanical model of nonextensive equilibrium thermodynamics for small interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature, we prove that it is an…

Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…

A formal correspondence between the q-distribution obtained from the Tsallis entropy and non-maxwellian distributions obtained from the Boltzmann-Gibbs entropy is afforded.

In an earlier study, we showed that Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to non-extensive systems, can be used as a possible risk measure in constructing risk optimal…

We show that an entanglement measure called relative entropy of entanglement satisfies a strong continuity condition. If two states are close to each other then so are their entanglements per particle pair in this measure. It follows in…

The fermionic relative entropy in two-dimensional Rindler spacetime is studied using both modular theory and the reduced one-particle density operators. The methods and results are compared. A formula for the relative entropy for general…

We extend the Hanel and Thurner asymptotic analysis to both extensive and non-extensive entropies on the basis of a wide class of entropic forms. The procedure is known to be capable to classify multiple entropy measures in terms of their…

Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…

We study the relation of relative topological entropy and relative mean dimension between a factor map and its induced factor map for amenable group actions. On the one hand, we prove that a factor map has zero relative topological entropy…

The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…

The paper extends the analysis of the entropies of the Poisson distribution with parameter $\lambda$. It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic behavior with respect to $\lambda$, whereas two generalized…

The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…

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…

Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…