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Annales Geophysicae An open-access journal of the European Geosciences Union
Ann. Geophys., 34, 1145-1158, 2016
http://www.ann-geophys.net/34/1145/2016/
doi:10.5194/angeo-34-1145-2016
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Regular paper
02 Dec 2016
Modeling anisotropic Maxwell–Jüttner distributions: derivation and properties
George Livadiotis Southwest Research Institute, San Antonio, Texas, USA
Abstract. 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.

Citation: Livadiotis, G.: Modeling anisotropic Maxwell–Jüttner distributions: derivation and properties, Ann. Geophys., 34, 1145-1158, doi:10.5194/angeo-34-1145-2016, 2016.
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Short summary
The paper develops a consistent model for the anisotropic Maxwell–Jüttner distribution. This is the velocity distribution in a gas of relativistic particles, where the temperature is not equi-distributed in all degrees of freedom. The physical requirements necessary for modeling this distribution are provided. The known models are examined showing that they do not fulfill these requirements, while a new model is constructed and studied that is consistent with all the required conditions.
The paper develops a consistent model for the anisotropic Maxwell–Jüttner distribution. This is...
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