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Open AccessArticle

Thermodynamic, Non-Extensive, or Turbulent Quasi-Equilibrium for the Space Plasma Environment

by Peter H. Yoon 1,2
1
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
2
Korea Astronomy and Space Science Institute, Daejeon 34055, Korea
Entropy 2019, 21(9), 820; https://doi.org/10.3390/e21090820
Received: 29 May 2019 / Revised: 21 August 2019 / Accepted: 21 August 2019 / Published: 22 August 2019
(This article belongs to the Special Issue Solar and Stellar Variability and Statistical Mechanics)
The Boltzmann–Gibbs (BG) entropy has been used in a wide variety of problems for more than a century. It is well known that BG entropy is additive and extensive, but for certain systems such as those dictated by long-range interactions, it is speculated that the entropy must be non-additive and non-extensive. Tsallis entropy possesses these characteristics, and is parameterized by a variable q ( q = 1 being the classic BG limit), but unless q is determined from microscopic dynamics, the model remains a phenomenological tool. To this day, very few examples have emerged in which q can be computed from first principles. This paper shows that the space plasma environment, which is governed by long-range collective electromagnetic interaction, represents a perfect example for which the q parameter can be computed from microphysics. By taking the electron velocity distribution function measured in the heliospheric environment into account, and considering them to be in a quasi-equilibrium state with electrostatic turbulence known as quasi-thermal noise, it is shown that the value corresponding to q = 9 / 13 = 0 . 6923 , or alternatively q = 5 / 9 = 0 . 5556 , may be deduced. This prediction is verified against observations made by spacecraft, and it is shown to be in excellent agreement. This paper constitutes an overview of recent developments regarding the non-equilibrium statistical mechanical approach to understanding the non-extensive nature of space plasma, although some recent new developments are also discussed. View Full-Text
Keywords: Kappa distribution; non-extensive entropy; plasma turbulence; solar wind; kinetic theory Kappa distribution; non-extensive entropy; plasma turbulence; solar wind; kinetic theory
MDPI and ACS Style

Yoon, P.H. Thermodynamic, Non-Extensive, or Turbulent Quasi-Equilibrium for the Space Plasma Environment. Entropy 2019, 21, 820.

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