1,721,030 research outputs found
q-generalized representation of the d-dimensional Dirac delta and q-Fourier transform
No full textWe introduce a generalized representation of the Dirac delta function in d dimensions in terms of q-exponential functions. We apply this new representation to the study of the so-called q-Fourier transform and we establish the analytical procedure through which it can be inverted for any value of d. We finally illustrate the effect of the q-deformation on the Gibbs phenomenon of Fourier series expansions
On the connection between linear combination of entropies and linear combination of extremizing distributions
No full textWe analyze the distribution that extremizes a linear combination of the Boltzmann–Gibbs entropy and the nonadditive q-entropy. We show that this distribution can be expressed in terms of a Lambert function. Both the entropic functional and the extremizing distribution can be associated with a nonlinear Fokker–Planck equation obtained from a master equation with nonlinear transition rates. Also, we evaluate the entropy extremized by a linear combination of a Gaussian distribution (which extremizes the Boltzmann–Gibbs entropy) and a q-Gaussian distribution (which extremizes the q-entropy). We give its explicit expression for q=0, and discuss the other cases numerically. The entropy that we obtain can be expressed, for q=0, in terms of Lambert functions, and exhibits a discontinuity in the second derivative for all values of q<1. The entire discussion is closely related to recent results for type-II superconductors and for the statistics of the standard map
Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution
No full textWe extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed
Linear instability and statistical laws of physics
No full text10.1209/epl/i2005-10248-2Europhysics Letters723355-36
On the robustness of the q-Gaussian family
No full textWe introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by Rodríguez et al. (2008), having q-Gaussians as N→ ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β-case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family
Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: a computational discussion
No full textWe implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs iota-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam beta-model, we show that at intermediate energies the Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law (F=ma). At higher energies we discuss partial agreement between time and ensemble averages
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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