Related papers: Weighted Approach to General Entropy Function
The entropy of probability distribution defined by Shannon has several extensions. R\'enyi entropy is one of the general extensions of Shannon entropy and is widely used in engineering, physics, and so on. On the other hand, the quantum…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
The definition of nonequilibrium entropy is provided for the general nonequilibrium processes by connecting thermodynamics with statistical physics, and the principle of entropy increment in the nonequilibrium processes is also proved in…
The problem of embedding the Tsallis and R\'{e}nyi entropies in the framework of category theory and their axiomatic foundation is studied. To this end, we construct a special category MES related to measured spaces. We prove that both of…
Given a general scalar balance law, i.e., in several space dimensions and with flux and source both space and time dependent, we focus on the functional properties of the entropy production. We apply this operator to entropy solutions, to…
The entropy is a measure of uncertainty that plays a central role in information theory. When the distribution of the data is unknown, an estimate of the entropy needs be obtained from the data sample itself. We propose a semi-parametric…
Tsallis relative operator entropy was defined as a parametric extension of relative operator entropy and the generalized Shannon inequalities were shown in the previous paper. After the review of some fundamental properties of Tsallis…
We characterize the inclusions of weighted classes of entire functions in terms of the defining weights resp. weight systems. First we treat weights defined in terms of a so-called associated weight function where the weight(system) is…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
The growing interest of different entropy functions proposed so far (like the Bekenstein-Hawking, Tsallis, R\'{e}nyi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies) towards black hole thermodynamics as well as towards…
The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy…
The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…
This paper proposes an extension of standard mixture stochastic models, by replacing the constant mixture weights with functional weights defined using a classifier. Classifier Weighted Mixtures enable straightforward density evaluation,…
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 unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
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 have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We show…