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A new q-deformed logistic map is proposed and it is found to have concavity in parts of the x-space. Its one-cycle and two-cycle non-trivial fixed points are obtained which are found to be qualitatively and quantitatively different from…

Chaotic Dynamics · Physics 2015-05-18 Subhashish Banerjee , R. Parthasarathy

This chapter deals with our recent attempt to extend the notion of equilibrium (EQ) entropy to nonequilibrium (NEQ) systems so that it can also capture memory effects. This is done by enlarging the equilibrium state space by introducing…

Statistical Mechanics · Physics 2022-01-03 P. D. Gujrati

We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' $q$-parametrized entropy. We discuss the dependence of the spacing distribution on $q$ using a non-extensive generalization of…

Statistical Mechanics · Physics 2007-05-23 A. Y. Abul-Magd

Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…

Computational Physics · Physics 2022-06-22 Jonah M. Miller , Joshua C. Dolence , Daniel Holladay

q-Gaussian distribution appear in many science areas where we can find systems that could be described within a nonextensive framework. Usually, a way to assert that these systems belongs to nonextensive framework is by means of numerical…

Data Analysis, Statistics and Probability · Physics 2017-03-21 Wagner S. de Lima , Emerson L. de Santa Helena

We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective…

Statistics Theory · Mathematics 2021-06-16 Steffen Betsch , Bruno Ebner , Bernhard Klar

In this work in progress, we study the asymptotic behaviour of the $p$-quantile of the Beta distribution, i.e. the quantity $q$ defined implicitly by $\int_0^q t^{a - 1} (1 - t)^{b - 1} \text{d} t = p B (a, b)$, as a function of the first…

Classical Analysis and ODEs · Mathematics 2017-09-22 Dimitris Askitis

The classic central limit theorem and $\alpha$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the…

Statistical Mechanics · Physics 2008-05-04 Sabir Umarov , Constantino Tsallis , Murray Gell-Mann , Stanly Steinberg

In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…

Statistical Mechanics · Physics 2007-05-23 John Evans , Fredrick Michael

The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. In this letter, the q-exponential of a sum can be applied as the product of the q-exponential…

Statistical Mechanics · Physics 2015-08-10 Jiulin Du

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…

Statistical Mechanics · Physics 2009-11-10 Constantino Tsallis

Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…

Mathematical Physics · Physics 2015-06-04 Miguel Ballesteros , Martin Fraas , Jürg Fröhlich , Baptiste Schubnel

We study the nonextensive parameter for the rotating astrophysical systems with power-law distributions, including both the rotating self-gravitating system and the rotating space plasma. We extend the equation of nonextensive parameter to…

Statistical Mechanics · Physics 2017-02-10 Haining Yu , Jiulin Du

Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…

History and Overview · Mathematics 2018-03-23 Cecilia Chirenti , M. Coleman Miller

We investigate a generalisation of the logistic map as $ x_{n+1}=1-ax_{n}\otimes_{q_{map}} x_{n}$ ($-1 \le x_{n} \le 1$, $0<a\le2$) where $\otimes_q$ stands for a generalisation of the ordinary product, known as $q$-product [Borges, E.P.…

Chaotic Dynamics · Physics 2011-12-20 Robson W. S. Pessoa , Ernesto P. Borges

In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments,…

Applications · Statistics 2016-11-25 Deepesh Bhati , Mohd. Aamir Malik

The problem of factorization of a nonextensive probability distribution is discussed. It is shown that, in general, the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the…

Statistical Mechanics · Physics 2007-05-23 Q. A. Wang , M. Pezeril , L. Nivanen , A. Le Mehaute

The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…

Statistical Mechanics · Physics 2016-04-20 A. Kononovicius , J. Ruseckas

A scheme of q-deformation of nonlinear maps is introduced. As a specific example, a q-deformation procedure related to the Tsallis q-exponential function is applied to the logistic map. Compared to the canonical logistic map, the resulting…

Chaotic Dynamics · Physics 2009-11-10 Ramaswamy Jaganathan , Sudeshna Sinha

We generalize some widely used mother wavelets by means of the q-exponential function $e_q^x \equiv [1+(1-q)x]^{1/(1-q)}$ ($q \in {\mathbb R}$, $e_1^x=e^x$) that emerges from nonextensive statistical mechanics. Particularly, we define…

Statistical Mechanics · Physics 2007-05-23 Ernesto P. Borges , Constantino Tsallis , Jose G. V. Miranda , Roberto F. S. Andrade