Related papers: On some entropy functionals derived from R\'enyi i…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…
We consider the two-dimensional (2d) Ising model on a infinitely long cylinder and study the probabilities $p_i$ to observe a given spin configuration $i$ along a circular section of the cylinder. These probabilities also occur as…
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…
With use of the Second Inverse Maximum Entropy Principle we find entropy functions for systems with fractal distribution functions with order parameter $q$. We compare these entropy functions with those given by the Bose-Einstein and…
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.…
Estimation of quantum relative entropy and its R\'{e}nyi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators of these divergences have been proposed in the…
This paper explores some applications of a two-moment inequality for the integral of the $r$-th power of a function, where $0 < r< 1$. The first contribution is an upper bound on the R\'{e}nyi entropy of a random vector in terms of the two…
Entropies must correspond to mean values for them to be measurable. The Shannon entropy corresponds to the weighted arithmetic mean, whereas the Renyi entropy corresponds to the exponential mean. These means refer to code lengths, which are…
There are no universally accepted definitions of R\'enyi conditional entropy and R\'enyi mutual information, although motivated by different applications, several definitions have been proposed in the literature. In this paper, we consider…
R\'enyi entropy is an important measure in the context of information theory as a generalization of Shannon entropy. This information measure was often used for uncertainty quantification of dynamical behaviour of stochastic processes. In…
The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation.…
The R\'enyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field $\lambda$ that controls the partition…
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 show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and…
Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the R\'enyi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation…