Derivation of the entropic formula for the statistical mechanics of space plasmas

Abstract

Abstract. Kappa distributions describe velocities and energies of plasma populations in space plasmas. The statistical origin of these distributions is associated with the framework of nonextensive statistical mechanics. Indeed, the kappa distribution is derived by maximizing the q entropy of Tsallis, under the constraints of the canonical ensemble. However, the question remains as to what the physical origin of this entropic formulation is. This paper shows that the q entropy can be derived by adapting the additivity of energy and entropy.

Electron mirror branch: observational evidence from “historical” AMPTE-IRM and Equator-S measurements

“…1 and 2. We repeat that these Eq-S chains of magnetic modulations had indeed been identified as mirror modes by Lucek et al (1999a), even though no plasma data were available. We also repeat that, even if the plasma instrument on Eq-S would have worked properly, its time resolution of ∼ 3 s would not have been sufficient to resolve any anti-correlation between the magnetic and plasma pressures in the oscillations which we here and below identify as electron mirror modes.…”

Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas

“…The kappa distributions have a tremendous number of applications in space and astrophysical plasmas, such as the inner heliosphere, including solar wind (e.g., [13,20,26,[38][39][40][41][42][43][44][45][46][47][48]), solar spectra (e.g., [49,50]), the solar corona (e.g., [51][52][53][54]), solar energetic particles (e.g., [55,56]), corotating interaction regions (e.g., [57]), and related solar flares (e.g., [21,33,58,59]); planetary magnetospheres, including the magnetosheath (e.g., [60,61]), magnetopause (e.g., [62]), magnetotail (e.g., [63]), ring current (e.g., [64]), plasma sheet (e.g., [65][66][67]), magnetospheric substorms (e.g., [68]), Aurora (e.g., [69]); magnetospheres of giant planets like the Jovian (e.g., [70][71][72]), Saturnian (e.g., [73][74][75][76]), Uranian (e.g., [77]), and Neptunian (e.g., <...>…”

“…The plethora of these applications stands on the fact that the kappa distributions are the most general formulations of particle velocity distributions that can be assigned with a temperature [13]. On the other hand, the kappa index that labels and governs these distributions constitutes a new thermodynamic variable, equally important as the temperature.…”

“…Note that the label q stands for the mono-parametrical entropy expressed in terms of q-index, or equivalently, in terms of kappa index, i.e., q ≡ 1 + 1/κ ⇔ κ = 1/(q − 1) [2]. On the other hand, the thermodynamic origin of these distributions and their associated entropy (the q-entropy) was also shown from first principles (e.g., see [13,14]); namely, the most generalized form of particle distribution function that can be assigned with a temperature is that of kappa distributions (or a combination thereof). Then, "thermalization" is the characterization of a particle system residing in any stationary state assigned by a temperature; in these states, the particle velocities or energies are stabilized into kappa distributions.…”

Slowing down of charged particles in dusty plasmas with power‐law kappa‐distributions

“…In solar wind plasmas, a log‐ κ distribution was introduced in order to replace the log‐normal distribution . Until now, the κ ‐distributions have aroused great concern for their new characteristics and interesting applications found in many fields of astrophysics, space plasmas, and laboratory plasmas, for example, κ ‐distribution in a superthermal radiation field plasma, a solar wind kinetic model based on the κ ‐distributions for electrons and protons escaping out of solar corona, Landau damping, ion acoustic waves and dust acoustic waves in space plasmas, fluctuations in magnetized plasmas with κ ‐distributions, some transport coefficients in κ ‐distributed plasmas, and properties of the κ ‐distributions in space plasmas. In particular, with the development of non‐extensive statistics, when it is recognized that this new statistical theory can be used as a theoretical basis for the study of power‐law distributed plasmas, the investigations of q‐ distributed plasmas will become increasingly widespread across both astrophysics and space science with an exponential growth rate of relevant publications (see the list of publications on plasma physics in ref.…”