170,243 research outputs found
Compatibility between dynamics and Tsallis statistics
No full textWe perform numerical simulations for the dynamics of a chain of weakly coupled particles, and consider the process of occupation of cells in phase space, in the spirit of paper [1]. A different behaviour is exhibited as the coupling constant is changed. It is discussed whether such a dynamical behaviour is compatible with the Tsallis statistics
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
Quasi-stationary states in low-dimensional Hamiltonian systems
No full textWe address a simple connection between results of Hamiltonian non-linear dynamical theory and thermostatistics. Using a properly defined dynamical temperature in low-dimensional symplectic maps, we display and characterize long-standing quasistationary states that eventually cross over to a Boltzmann-Gibbs-like regime. As time evolves, the geometrical properties (e.g., fractal dimension) of the phase space change sensibly, and the duration of the anomalous regime diverges with decreasing chaoticity. The scenario that emerges is consistent with the non-extensive statistical mechanics one. (C) 2003 Elsevier B.V. All rights reserved
Linear instability and statistical laws of physics
No full text10.1209/epl/i2005-10248-2Europhysics Letters723355-36
Integrable multi-phase thermodynamic systems and Tsallis' composition rule
No full textWe derive a class of equations of state for a multi-phase thermodynamic system associated with a finite set of order parameters that satisfy an integrable system of hydrodynamic type. As particular examples, we discuss one-phase systems
such as the van der Waals gas and the effective molecular field model. The case of phase systems is also discussed in detail in connection with entropies depending on the order parameter according to Tsallis' composition rule
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
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
Fractal growth of carbon schwarzites
No full textThe potential energy, the thermodynamic properties and the growth conditions of random carbon schwarzites are theoretically investigated in connection with their topological properties and self-affine structure. An analysis based on numerical simulations of transmission electron microscopy images permits to assign certain carbon foams, recently produced by means of supersonic cluster beam deposition, to self-affine random schwarzites. It is shown that self-affinity makes their thermodynamic properties non-extensive. The fractal growth exponent is shown to be related to the parameter q -1 of the Tsallis non-extensive entropy
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
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