Related papers: Shannon and Renyi Entropy of Wavelets
The Wehrl entropy of a quantum state is the Shannon entropy of its coherent-state distribution function, and remains non-zero even for pure states. We investigate the relationship between this entropy and the many-particle quantum…
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…
The Renyi entropy with a free Renyi parameter $q$ is the most justified form of information entropy, and the Tsallis entropy may be regarded as a linear approximation to the Renyi entropy when $q\simeq 1$. When $q\to 1$, both entropies go…
We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing R\'enyi entropies of order $\eta$, of which Shannon entropy is the special case $\eta=1$. The order of R\'enyi entropy is determined by the…
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we…
We calculate explicit formulae for the Shannon entropies of several families of tailored random graph ensembles for which no such formulae were as yet available, in leading orders in the system size. These include bipartite graph ensembles…
The uncertainty relation based on the Shannon entropies of the probability densities in position and momentum spaces is improved for quantum systems in arbitrary $D$-dimensional spherically symmetric potentials. To find it, we have used the…
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
We consider a probability distribution depending on a real parameter $x$. As functions of $x$, the R\'enyi entropy and the Tsallis entropy can be expressed in terms of the associated index of coincidence $S(x)$. We establish recurrence…
We calculate analytically the Renyi entropy for the zeta-urn model with a Gibbs measure definition of the micro-state probabilities. This allows us to obtain the singularities in the R\'enyi entropy from those of the thermodynamic…
We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs--Shannon entropy into more general framework - Renyi's information entropy. We address the…
We introduce the problem of \emph{entropy equivalence testing} for probability distributions, a relaxation of the well-studied closeness testing problem, where the distribution testing algorithm is now only required to distinguish, given…
The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is…
This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational…
The fundamental information-theoretic measures (the R\'enyi $R_{p}[\rho]$ and Tsallis $T_{p}[\rho]$ entropies, $p>0$) of the highly-excited (Rydberg) quantum states of the $D$-dimensional ($D>1$) hydrogenic systems, which include the…
The aim of the paper is to study the link between non additivity of some entropies and their boundedness. We propose an axiomatic construction of the entropy relying on the fact that entropy belongs to a group isomorphic to the usual…
The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak…
We develop the most probable wave functions for a single free quantum particle given its momentum and energy by imposing its quantum probability density to maximize Shannon information entropy. We show that there is a class of solutions in…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by…