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Related papers: Axioms and uniqueness theorem for Tsallis entropy

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A method of estimating the joint probability mass function of a pair of discrete random variables is described. This estimator is used to construct the conditional Shannon-R\'eyni-Tsallis entropies estimates. From there almost sure rates of…

Statistics Theory · Mathematics 2020-02-18 Ba Amadou Diadie , Lo Gane Samb

We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…

Disordered Systems and Neural Networks · Physics 2007-11-20 Fariel Shafee

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…

Quantum Physics · Physics 2017-01-04 Mirjam Weilenmann , Lea Krämer , Philippe Faist , Renato Renner

A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…

Statistical Mechanics · Physics 2025-02-20 O. K. Kazemi , S. M. Taheri

We adapt the Kolmogorov-Sinai entropy to the non-extensive perspective recently advocated by Tsallis. The resulting expression is an average on the invariant distribution, which should be used to detect the genuine entropic index Q. We…

Condensed Matter · Physics 2009-10-31 Jin Yang , Paolo Grigolini

A new concept named nonsymmetric entropy which generalizes the concepts of Boltzman's entropy and shannon's entropy, was introduced. Maximal nonsymmetric entropy principle was proven. Some important distribution laws were derived naturally…

Information Theory · Computer Science 2007-07-13 Chengshi Liu

It is shown that the distribution derived from the principle of maximum Tsallis entropy is a superposable Levy-type distribution. Concomitantly, the leading order correction to the limit distribution is also deduced. This demonstration…

Statistical Mechanics · Physics 2007-05-23 Sumiyoshi Abe , A. K. Rajagopal

We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…

Quantum Physics · Physics 2018-05-30 Alexey E. Rastegin

We generalize the completely monotone conjecture ([CG15]) from Shannon entropy to the Tsallis entropy up for orders up to at least four. To this end, we employ the algorithm ([J\"un16, JM06a]) which employs the technique of systematic…

Analysis of PDEs · Mathematics 2022-12-20 Li-Chang Hung

In this paper, we propose a new discriminative model named \emph{nonextensive information theoretical machine (NITM)} based on nonextensive generalization of Shannon information theory. In NITM, weight parameters are treated as random…

Machine Learning · Computer Science 2016-04-22 Chaobing Song , Shu-Tao Xia

Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…

Quantitative Methods · Quantitative Biology 2022-02-08 Keisuke Okamura

We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system,…

Quantum Physics · Physics 2015-05-20 N. Canosa , R. Rossignoli

Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…

Quantum Physics · Physics 2010-05-04 Anthony J. Short , Stephanie Wehner

The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we present the regular solution of these equations, as well.…

Classical Analysis and ODEs · Mathematics 2013-07-03 Eszter Gselmann

Whereas Shannon entropy is related to the growth rate of multinomial coefficients, we show that the quadratic entropy (Tsallis 2-entropy) is connected to their $q$-deformation; when $q$ is a prime power, these $q$-multinomial coefficients…

Mathematical Physics · Physics 2020-03-27 Juan Pablo Vigneaux

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…

Information Theory · Computer Science 2019-09-04 Kohtaro Tadaki

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…

Statistical Mechanics · Physics 2009-11-13 Hideo Hasegawa

When at equilibrium, large-scale systems obey conventional thermodynamics because they belong to microscopic configurations (or states) that are typical. Crucially, the typical states usually represent only a small fraction of the total…

Statistical Mechanics · Physics 2025-01-14 Bernat Corominas-Murtra , Rudolf Hanel , Petr Jizba

A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…

Chaotic Dynamics · Physics 2009-11-10 Henk van Beijeren

We discuss the entropic criterion for separability of compound quantum systems for general non-additive entropic forms based on arbitrary concave functions $f$. For any separable state, the generalized entropy of the whole system is shown…

Quantum Physics · Physics 2015-05-20 R. Rossignoli , N. Canosa