Related papers: Information Entropy, Information Distances and Com…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential…
We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional…
We compare the elementary theories of Shannon information and Kolmogorov complexity, the extent to which they have a common purpose, and where they are fundamentally different. We discuss and relate the basic notions of both theories:…
A two parameter generalization of Boltzmann-Gibbs-Shannon entropy based on natural logarithm is introduced. The generalization of the Shannon-Kinchinn axioms corresponding to the two parameter entropy is proposed and verified. We present…
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
The Shannon entropy of a random variable has much behaviour analogous to a signed measure. Previous work has explored this connection by defining a signed measure on abstract sets, which are taken to represent the information that different…
The Shannon based conditional entropy that underlies five-dimensional Einstein-Hilbert gravity coupled to a dilaton field is investigated in the context of dynamical holographic AdS/QCD models. Considering the UV and IR dominance limits of…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…
An overview of the Bose-Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the…
We aim to quantify the distribution of information in the Hawking radiation and inside the black hole in the semiclassical evaporation process. The structure quantum field theory forces to consider a shared information between two different…
It is usually stated that the information storing region associated with the Bekenstein-Hawking entropy is enclosed by a sphere of diameter equal twice the Schwarzschild radius. We point out that this cannot apply to a quantum black hole.…
According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials…
We present analytical estimates and numerical calculations showing that the energy level density in open-shell atoms increases exponentially with increase of excitation energy. As an example, we use the relativistic Hartree-Fock and…
Shannon's entropy is one of the building blocks of information theory and an essential aspect of Machine Learning methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable…
The paper presents an extension of Shannon entropy for neutrosophic information. This extension uses a new formula for distance between two neutrosophic triplets. In addition, the obtained results are particularized for bifuzzy,…