Abstract
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 ( 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 , or alternatively , 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.
Highlights
The celebrated Boltzmann–Gibbs (BG) definition for entropy [1,2], SBG = k log W, (1)has been used in a wide variety of problems for more than a century
The finding that quasi-steady-state plasma turbulence corresponds to the kappa distribution function strongly implies the profound inter-relationship with a non-extensive statistical equilibrium
We move on to the section, where we discuss the asymptotically steady-state electrostatic plasma turbulence and the corresponding electron velocity distribution. It is the purpose of the present paper to overview recent developments in the theory of the electron kappa distribution in space from the perspective of non-equilibrium statistical mechanics
Summary
The finding that quasi-steady-state plasma turbulence corresponds to the kappa distribution function strongly implies the profound inter-relationship with a non-extensive statistical equilibrium. Quasi-equilibrium states of plasma turbulence depict electrons interacting amongst themselves through long-range collective electrostatic fluctuations, which describes the non-extensive charged-particle system interacting with long-range electrostatic force. We move on to the section, where we discuss the asymptotically steady-state electrostatic plasma turbulence and the corresponding electron velocity distribution It is the purpose of the present paper to overview recent developments in the theory of the electron kappa distribution in space from the perspective of non-equilibrium statistical mechanics. Some new developments will be discussed, including the question of the transition from the kappa distribution to an eventual thermal distribution and the modification of the standard kappa distribution as well as its consequences on observed charged particle distributions in space
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