Abstract
Abstract. Non-extensive systems, accounting for long-range interactions and correlations, are fundamentally related to non-Maxwellian distributions where a duality of equilibria appears in two families, the non-extensive thermodynamic equilibria and the kinetic equilibria. Both states emerge out of particular entropy generalization leading to a class of probability distributions, where bifurcation into two stationary states is naturally introduced by finite positive or negative values of the involved entropic index kappa. The limiting Boltzmann-Gibbs-Shannon state (BGS), neglecting any kind of interactions within the system, is subject to infinite entropic index and thus characterized by self-duality. Fundamental consequences of non-extensive entropy bifurcation, manifest in different astrophysical environments, as particular core-halo patterns of solar wind velocity distributions, the probability distributions of the differences of the fluctuations in plasma turbulence as well as the structure of density distributions in stellar gravitational equilibrium are discussed. In all cases a lower entropy core is accompanied by a higher entropy halo state as compared to the standard BGS solution. Data analysis and comparison with high resolution observations significantly support the theoretical requirement of non-extensive entropy generalization when dealing with systems subject to long-range interactions and correlations.
Highlights
Power-law behavior as manifestation of fractal or multifractal structures is found in a great variety of complex phenomena in different scientific fields
Leptokurtic, long-tailed probability distribution functions (PDF’s) subject to a non-Gaussian core and a pronounced halo are a persistent feature in a variety of different astrophysical environments
The accuracy of the bi-kappa distribution fits clearly indicates that non-locality in turbulence, when introduced theoretically by long-range interactions through a nonextensive entropy generalization, provides a precise representation of the observed PDFs characterizing the intermittency of the magnetic field fluctuations at all scales
Summary
Power-law behavior as manifestation of fractal or multifractal structures is found in a great variety of complex phenomena in different scientific fields. Leptokurtic, long-tailed probability distribution functions (PDF’s) subject to a non-Gaussian core and a pronounced halo are a persistent feature in a variety of different astrophysical environments. Those include the thermo-statistical properties of the interplanetary medium where the electron, proton and even heavy ion velocity space distributions show ubiquitously suprathermal halo patterns (see Mendis and Rosenberg (1994) for a general review, or Leubner (2000); Leubner and Schupfer (2001) and references therein), well described by the empirical family of κ-distributions, a power law in particle speed and first recognized by Vasyliunas (1968). Nonextensive statistics is tested on three fundamentally different physical situations: (1) the free solar wind distributions in velocity space, (2) the probability distributions of fluctuations in turbulence and (3) the radial density distributions of gravitationally clustered structures
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