294 research outputs found

    An amended MaxEnt formulation for deriving Tsallis factors, and associated issues

    Get PDF
    An amended MaxEnt formulation for systems displaced from the conventional MaxEnt equilibrium is proposed. This formulation involves the minimization of the Kullback-Leibler divergence to a reference QQ (or maximization of Shannon QQ-entropy), subject to a constraint that implicates a second reference distribution P_1P\_{1} and tunes the new equilibrium. In this setting, the equilibrium distribution is the generalized escort distribution associated to P_1P\_{1} and QQ. The account of an additional constraint, an observable given by a statistical mean, leads to the maximization of R\'{e}nyi/Tsallis QQ-entropy subject to that constraint. Two natural scenarii for this observation constraint are considered, and the classical and generalized constraint of nonextensive statistics are recovered. The solutions to the maximization of R\'{e}nyi QQ-entropy subject to the two types of constraints are derived. These optimum distributions, that are Levy-like distributions, are self-referential. We then propose two `alternate' (but effectively computable) dual functions, whose maximizations enable to identify the optimum parameters. Finally, a duality between solutions and the underlying Legendre structure are presented.Comment: Presented at MaxEnt2006, Paris, France, july 10-13, 200

    Superdiffusion in Decoupled Continuous Time Random Walks

    Full text link
    Continuous time random walk models with decoupled waiting time density are studied. When the spatial one jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized superdiffusive regime is established. This is verified by showing that the square width of the probability distribution (appropriately defined)grows as t2/γt^{2/\gamma} with 0<γ20<\gamma\leq2 when tt\to \infty. An important connection of our results and those of Tsallis' nonextensive statistics is shown. The normalized q-expectation value of x2x^2 calculated with the corresponding probability distribution behaves exactly as t2/γt^{2/\gamma} in the asymptotic limit.Comment: 9 pages (.tex file), 1 Postscript figures, uses revtex.st

    Quantal distribution functions in non-extensive statistics and an early universe test revisited

    Full text link
    Within the context of non-extensive thermostatistics, we use the factorization approximation to study a recently proposed early universe test. A very restrictive bound upon the non-extensive parameter is presented: q1<4.01×103|q-1| < 4.01 \times 10^{-3}.Comment: 4 pages, prl revtex style, no figures. To appear in Physica A, 199

    Microscopic dynamics underlying the anomalous diffusion

    Full text link
    The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347 (1995)]. The scope of the present paper is twofold. Firstly we show that this distribution can be obtained also as solution of the non-linear porous media equation. Secondly we prove that the time dependent Tsallis distribution can be obtained also as solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the velocity, that describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200

    Microscopic dynamics underlying the anomalous diffusion

    Full text link
    The time dependent Tsallis statistical distribution describing anomalous diffusion is usually obtained in the literature as the solution of a non-linear Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347 (1995)]. The scope of the present paper is twofold. Firstly we show that this distribution can be obtained also as solution of the non-linear porous media equation. Secondly we prove that the time dependent Tsallis distribution can be obtained also as solution of a linear FP equation [G. Kaniadakis and P. Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the velocity, that describes a generalized Brownian motion. This linear FP equation is shown to arise from a microscopic dynamics governed by a standard Langevin equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200

    Thermodynamic Description of the Relaxation of Two-Dimensional Euler Turbulence Using Tsallis Statistics

    Full text link
    Euler turbulence has been experimentally observed to relax to a metaequilibrium state that does not maximize the Boltzmann entropy, but rather seems to minimize enstrophy. We show that a recent generalization of thermodynamics and statistics due to Tsallis is capable of explaining this phenomenon in a natural way. The maximization of the generalized entropy S1/2S_{1/2} for this system leads to precisely the same profiles predicted by the Restricted Minimum Enstrophy theory of Huang and Driscoll. This makes possible the construction of a comprehensive thermodynamic description of Euler turbulence.Comment: 15 pages, RevTe

    Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part one: Sunspot dynamics

    Full text link
    In this study, the nonlinear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis. The triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum, the generalized Renyi dimension spectrum and the spectrum of the structure function exponents were estimated experimentally and theoretically by using the entropy principle included in Tsallis non extensive statistical theory, following Arimitsu and Arimitsu. Our analysis showed clearly the following: a) a phase transition process in the solar dynamics from high dimensional non Gaussian SOC state to a low dimensional non Gaussian chaotic state, b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov studies c) faithful agreement of Tsallis non equilibrium statistical theory with the experimental estimations of i) non-Gaussian probability distribution function, ii) multifractal scaling exponent spectrum and generalized Renyi dimension spectrum, iii) exponent spectrum of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.Comment: 40 pages, 11 figure

    Nonextensive Thermostatistics and the H-Theorem

    Full text link
    The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the ``molecular chaos hypothesis". For q>0q>0, the qq-transport equation satisfies an HH-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' qq-nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo

    Interstellar Sonic and Alfv\'enic Mach Numbers and the Tsallis Distribution

    Full text link
    In an effort to characterize the Mach numbers of ISM magnetohydrodynamic (MHD) turbulence, we study the probability distribution functions (PDFs) of patial increments of density, velocity, and magnetic field for fourteen ideal isothermal MHD simulations at resolution 512^3. In particular, we fit the PDFs using the Tsallis function and study the dependency of fit parameters on the compressibility and magnetization of the gas. We find that the Tsallis function fits PDFs of MHD turbulence well, with fit parameters showing sensitivities to the sonic and Alfven Mach numbers. For 3D density, column density, and position-position-velocity (PPV) data we find that the amplitude and width of the PDFs shows a dependency on the sonic Mach number. We also find the width of the PDF is sensitive to global Alfvenic Mach number especially in cases where the sonic number is high. These dependencies are also found for mock observational cases, where cloud-like boundary conditions, smoothing, and noise are introduced. The ability of Tsallis statistics to characterize sonic and Alfvenic Mach numbers of simulated ISM turbulence point to it being a useful tool in the analysis of the observed ISM, especially when used simultaneously with other statistical techniques.Comment: 20 pages, 16 figures, ApJ submitte

    Generalized quantal distribution functions within factorization approach: Some general results for bosons and fermions

    Full text link
    The generalized quantal distribution functions are investigated concerning systems of non-interacting bosons and fermions. The formulae for the number of particles and energy are presented and applications to the Chandrasekhar limit of white dwarfs stars and to the Bose-Einstein condensation are commented.Comment: 10 pages, prl revtex style, 2 ps figure
    corecore