Related papers: Generalized Shannon inequalities based on Tsallis …
A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…
An amended MaxEnt formulation for systems displaced from the conventional MaxEnt equilibrium is proposed. This formulation involves the minimization of the Kullback-Leibler divergence to a reference $Q$ (or maximization of Shannon…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
In this paper we obtain generalized Gronwall type inequality using Caputo Fractional delta operator. Also we have obtained the existence of solution of Cauchy's Type problem on fractional dynamic equations using dynamic delta operator.…
The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev's axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin's axiom in…
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…
We study the properties of Tsallis entropy and Shannon entropy from the point of view of algorithmic randomness. In algorithmic information theory, there are two equivalent ways to define the program-size complexity K(s) of a given finite…
The problem of Shannon entropy estimation in countable infinite alphabets is addressed from the study and use of convergence results of the entropy functional, which is known to be discontinuous with respect to the total variation distance…
A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases…
We consider the concept of generalized measure-theoretic entropy, where instead of the Shannon entropy function we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this…
We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of…
Generalized numbers, arithmetic operators and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of $q$-logarithm/$q$-exponential inverse functions. Some of the…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter $q$. A number of possible sources of such distributions are presented in more detail. It is further…
In this paper we present a new type of fractional operator, which is a generalization of the Caputo and Caputo--Hadamard fractional derivative operators. We study some properties of the operator, namely we prove that it is the inverse…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
First the Hardy and Rellich inequalities are defined for the submarkovian operator associated with a local Dirichlet form. Secondly, two general conditions are derived which are sufficient to deduce the Rellich inequality from the Hardy…
We provide generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Using quantum Tsallis entropy of order $q$, we first provide a generalized monogamy inequality of multi-qubit entanglement for $q=2$ or $3$.…
We obtain optimal generalized versions of Hardy inequalities, which as special cases contain Hardy's inequality and Hardy's inequality involving the distance function to the boundary of $ \Omega$. In addition we obtain neccesary and…