Non-equilibrium statistical mechanical approach to the formation of non-Maxwellian electron distribution in space

• Published in: The European physical journal. ST, Special topics Vol. 229; no. 5; pp. 819 - 840
• Main Author: Yoon, Peter H.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V
• Subjects: Atomic; Charged particles; Classical and Continuum Physics; Condensed Matter Physics; Distribution functions; Electron distribution; Entropy; Materials Science; Measurement Science and Instrumentation; Molecular; Nonextensive Statistical Mechanics; Normal distribution; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article; Space plasmas; Statistical analysis; Superstatistics and Beyond: Theory & Applications in Astrophysical and Other Complex Systems
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2020-900215-4

Boltzmann-Gibbs (BG) entropy has additive and extensive properties, but for certain physical systems, such as those governed by long-range interactions – plasma or fully ionized gas being an example – it is speculated that the entropy must be non-additive and non-extensive. Because of the fact that Tsallis entropy possesses such characteristics, many spacecraft observations of charged particle distributions in space are interpreted with the conceptual framework based upon Tsallis statistical principles. This paper formulates the non-equilibrium statistical theory of space plasma, and it is shown that the steady state electrostatic turbulence in plasma coincides with the formation of non-Maxwellian electron distribution function known as the kappa distribution. The kappa distribution is equivalent to the q -Gaussian distribution in the Tsallis statistical theory, which represents the most probable state subject to Tsallis entropy. This finding represents an independent confirmation that the space plasma may indeed be governed by the Tsallis statistical principle.