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

2017 ◽  
Author(s):  
George Livadiotis
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble ◽  
Space Plasmas ◽  
Kappa Distribution ◽  
Physical Origin

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

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

2018 ◽  
Vol 25 (1) ◽  
pp. 77-88 ◽  
Author(s):  
George Livadiotis
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble ◽  
Space Plasmas ◽  
Kappa Distribution ◽  
Physical Origin ◽  
Nonextensive Statistical Mechanics

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.

Statistical mechanics of Fermi-Pasta-Ulam chains with the canonical ensemble

1997 ◽  
Vol 55 (3) ◽  
pp. 3727-3730
Author(s):  
Melik C. Demirel ◽  
Mehmet Sayar ◽  
Ali R. Atılgan
Keyword(s):  
Statistical Mechanics ◽  
Canonical Ensemble

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

Universe ◽  
2018 ◽  
Vol 4 (12) ◽  
pp. 144 ◽  
Author(s):  
George Livadiotis
Keyword(s):  
First Principles ◽  
Statistical Physics ◽  
Order Differential Equation ◽  
Canonical Ensemble ◽  
Space Plasmas ◽  
Astrophysical Plasmas ◽  
Particle Distributions ◽  
First Order ◽  
Continuous Description ◽  
Kappa Distribution Function

Kappa distributions received impetus as they provide efficient modelling of the observed particle distributions in space and astrophysical plasmas throughout the heliosphere. This paper presents (i) the connection of kappa distributions with statistical mechanics, by maximizing the associated q-entropy under the constraints of the canonical ensemble within the framework of continuous description; (ii) the derivation of q-entropy from first principles that characterize space plasmas, the additivity of energy, and entropy; and (iii) the derivation of the characteristic first order differential equation, whose solution is the kappa distribution function.

A dielectric tensor for a uniform magnetoplasma with a generalized Lorentzian distribution

1996 ◽  
Vol 55 (3) ◽  
pp. 415-429 ◽  
Author(s):  
R. L. Mace
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Magnetized Plasma ◽  
Space Plasmas ◽  
Dielectric Tensor ◽  
Kappa Distribution ◽  
Numerical Studies ◽  
Starting Point ◽  
Limiting Case ◽  
The Magnetic Field

It is demonstrated that the dielectric tensor for a non-relativistic magnetized plasma whose particle velocity distributions can be modelled by isotropic kappa, or generalized Lorentzian, distributions admits an expression similar to that obtained by Trubnikov for a relativistic plasma. The kappa distribution is a useful distribution for modelling space plasmas containing significant numbers of superthermal particles, i.e. those that have energies in excess of the thermal energy. The dielectric tensor is valid for arbitrary wavevectors, and is shown to reproduce the known limiting case of wave propagation parallel to the magnetic field. Even in this limiting case, the results obtained represent a generalization of previous results to arbitrary real values of the index K, the parameter that shapes the superthermal tail on the distribution. The expression for the dielectric tensor might be useful as a starting point for numerical studies of waves and instabilities in plasmas containing superthermal particles.

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