Related papers: A two-parameter entropy and its fundamental proper…
We analyze systematically composable composite entropy of two Tsallis subsystems with different q indices. H-theorem and thermal balance relation are commented.
Recently, Suyari has proposed a generalization of Shannon-Khinchin axioms, which determines a class of entropies containing the well-known Tsalis and Havrda-Charvat entropies [H. Suyari, IEEE Trans. Inf. Theory, vol. 50, pp. 1783-1787, Aug.…
It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and…
We have discussed dynamical properties of the Tsallis entropy and the generalized Fisher information in nonextensive systems described by the Langevin model subjected to additive and multiplicative noise. Analytical expressions for the…
We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.
The fractal and self-similarity properties are revealed in many complex networks. In order to show the influence of different part in the complex networks to the information dimension, we have proposed a new information dimension based on…
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…
Tsallis relative operator entropy is defined and then its properties are given. Shannon inequality and its reverse one in Hilbert space operators derived by T.Furuta \cite{Fu:par} are extended in terms of the parameter of the Tsallis…
We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes inequality.
The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and…
Information decompositions quantify how the Shannon information about a given random variable is distributed among several other random variables. Various requirements have been proposed that such a decomposition should satisfy, leading to…
In this paper we introduce a biparametric family of transformations which can be seen as an extension of the so-called up and down transformations. This new class of transformations allows to us to introduce new informational functionals,…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…
A comparative study of one-dimensional quantum structures which allow analytic expressions for the position and momentum R\'{e}nyi $R(\alpha)$ and Tsallis $T(\alpha)$ entropies, focuses on extracting the most characteristic physical…
In this paper we give an interpretation of Tsallis' nonextensive statistical mechanics based upon the information-theoretic point of view of Luzzi et al. [cond-mat/0306217; cond-mat/0306247; cond-mat/0307325], suggesting Tsallis' entropy to…
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…
This article consists of a very short introduction to classical and quantum information theory. Basic properties of the classical Shannon entropy and the quantum von Neumann entropy are described, along with related concepts such as…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…