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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 15, issue 4
Nonlin. Processes Geophys., 15, 531–540, 2008
https://doi.org/10.5194/npg-15-531-2008
© Author(s) 2008. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Nonlinear waves and turbulence in space

Nonlin. Processes Geophys., 15, 531–540, 2008
https://doi.org/10.5194/npg-15-531-2008
© Author(s) 2008. This work is distributed under
the Creative Commons Attribution 3.0 License.

  04 Jul 2008

04 Jul 2008

Consequences of entropy bifurcation in non-Maxwellian astrophysical environments

M. P. Leubner M. P. Leubner
  • Institute for Astro- and Particle Physics, University of Innsbruck, Innsbruck, Austria

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.

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