Modeling anisotropic Maxwell-Jüttner distributions: Derivation and properties

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In this paper we develop a model for the anisotropic Maxwell-Jüttner distribution and examine its properties. First, we provide the characteristic conditions that the modeling of consistent and well-defined anisotropic Maxwell-Jüttner distributions needs to fulfill. Then, we examine several models, showing their possible advantages and/or failures in accordance to these conditions. We derive a consistent model, and examine its properties and its connection with thermodynamics. We show that the temperature equals the average of the directional temperature-like components, as it holds for the classical, anisotropic Maxwell distribution. We also derive the internal energy and Boltzmann-Gibbs entropy, where we show that both are maximized for zero anisotropy, that is, the isotropic Maxwell-Jüttner distribution.

Original languageEnglish (US)
Pages (from-to)1145-1158
Number of pages14
JournalAnnales Geophysicae
Issue number12
StatePublished - Dec 2 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Geology
  • Atmospheric Science
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science


  • Electromagnetics (plasmas)
  • solar physics astrophysics and astronomy (magnetic fields)
  • space plasma physics (kinetic and MHD theory)


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