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

Livadiotis, G.

doi:10.3390/universe4120144

Cited by 20 publications

(12 citation statements)

References 130 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been shown that the pseudo-additivity rule is equivalent to the Tsallis entropy and to the formulation of kappa distributions: First, we recall that Tsallis entropy [ 18 , 19 , 20 ]) is equivalent to the formulation of kappa distributions (e.g., [ 5 , 21 , 22 , 23 , 24 ]; see also: [ 25 , 26 , 27 ] and [ 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 ]); indeed, this entropic formulation is maximized under the constraints of canonical ensemble leading to kappa distributions [ 5 ], and vice versa, when maximized, the entropic formulation leads to the specific form of kappa distributions [ 37 , 38 ]. Then, it can be easily shown that the Tsallis entropic function obeys to the pseudo-additivity rule [ 18 ].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect

Livadiotis

McComas

2021

Entropy

Self Cite

View full text Add to dashboard Cite

This paper develops explicit and consistent definitions of the independent thermodynamic properties of temperature and the kappa index within the framework of nonextensive statistical mechanics and shows their connection with the formalism of kappa distributions. By defining the “entropy defect” in the composition of a system, we show how the nonextensive entropy of systems with correlations differs from the sum of the entropies of their constituents of these systems. A system is composed extensively when its elementary subsystems are independent, interacting with no correlations; this leads to an extensive system entropy, which is simply the sum of the subsystem entropies. In contrast, a system is composed nonextensively when its elementary subsystems are connected through long-range interactions that produce correlations. This leads to an entropy defect that quantifies the missing entropy, analogous to the mass defect that quantifies the mass (energy) associated with assembling subatomic particles. We develop thermodynamic definitions of kappa and temperature that connect with the corresponding kinetic definitions originated from kappa distributions. Finally, we show that the entropy of a system, composed by a number of subsystems with correlations, is determined using both discrete and continuous descriptions, and find: (i) the resulted entropic form expressed in terms of thermodynamic parameters; (ii) an optimal relationship between kappa and temperature; and (iii) the correlation coefficient to be inversely proportional to the temperature logarithm.

show abstract

Section: Introductionmentioning

confidence: 99%

Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect

Livadiotis

McComas

2021

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…Conventionally, their evolution under nonstationary conditions, in particular in application to particle acceleration, is attributed to a Fokker-Planck description which naturally generates tails on the distribution function via momentum space diffusion. More basic theories have also been developed based on nonequilibrium statistical mechanics where they arise as stationary states far from thermal equilibrium [24][25][26][27][28]. In the asymptotic limit, nonlinear plasma theories [29][30][31] provide classical distributions of this kind.…”

Section: Introductionmentioning

confidence: 99%

Olbert’s Kappa Fermi and Bose Distributions

Treumann

Baumjohann

2021

Front. Phys.

View full text Add to dashboard Cite

The quantum version of Olbert’s kappa distribution applicable to fermions is obtained. Its construction is straightforward but requires recognition of the differences in the nature of states separated by Fermi momenta. Its complement, the bosonic version of the kappa distribution is also given, as is the procedure of how to construct a hypothetical kappa-anyon distribution. At very low temperature the degenerate kappa Fermi distribution yields a kappa-modified version of the ordinary degenerate Fermi energy and momentum. We provide the Olbert-generalized expressions of the Olbert-Fermi partition function and entropy which may serve determining all relevant statistical mechanical quantities. Possible applications are envisaged to condensed matter physics, possibly quantum plasmas, and dense astrophysical objects like the interior state of terrestrial planets, neutron stars, magnetars where quantum effects come into play and dominate the microscopic scale but may have macroscopic consequences.

show abstract

“…This simplified assumption could be justified based on the fact that large deviations from Maxwellian EVDFs are not sustainable for a long time in collisionless plasmas, because micro-instabilities feeding from those deviations tend to restore the EVDFs back into a Maxwellian one. One distribution that combines both low-energy Maxwellian and high-energy non-Maxwellian features is the Kappa distribution, which has been extensively applied to collisionless space and astrophysical plasmas 78,79 . Mathematically speaking, a single population of Kappa distribution can be approximately decomposed in a sum of a a central Gaussian distribution function to fit the core and another Gaussian distribution function with large width to fit its wide tail.…”

Section: B Diagnosticsmentioning

confidence: 99%

Formation of non-thermal electron velocity distribution functions in kinetic magnetic reconnection

Yao¹,

Muñoz²,

Büchner³

2021

Preprint

View full text Add to dashboard Cite

<div> <div>Magnetic reconnection can convert magnetic energy into non-thermal particle energy in the form of electron beams. Those accelerated electrons can, in turn, cause radio emission in environments such as solar flares. The actual properties of those electron velocity distribution functions (EVDFs) generated by reconnection are still not well understood. In particular the properties that are relevant for the micro-instabilities responsible for radio emission. We aim thus at characterizing the electron distributions functions generated by 3D magnetic reconnection by means of fully kinetic particle-in-cell (PIC) code simulations. Our goal is to characterize the possible sources of free energy of the generated EVDFs in dependence on an external (guide) magnetic field strength. We find that: (1) electron beams with positive gradients in their parallel (to the local magnetic field direction) distribution functions are observed in both diffusion region (parallel crescent-shaped EVDFs) and separatrices (bump-on-tail EVDFs). These non-thermal EVDFs cause counterstreaming and bump-on-tail instabilities. These electrons are adiabatic and preferentially accelerated by a parallel electric field in regions where the magnetic moment is conserved. (2) electron beams with positive gradients in their perpendicular distribution functions are observed in regions with weak magnetic field strength near the current sheet midplane. The characteristic crescent-shaped EVDFs (in perpendicular velocity space) are observed in the diffusion region. These non-thermal EVDFs can cause electron cyclotron maser instabilities. These non-thermal electrons in perpendicular velocity space are mainly non-adiabatic. Their EVDFs are attributed to electrons experiencing an E&#215;B drift and meandering motion. (3) As the guide field strength increases, the number of locations in the current sheet with distributions functions featuring a perpendicular source of free energy significantly decreases.</div> </div>

show abstract

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

Cited by 20 publications

References 130 publications

Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect

Thermodynamic Definitions of Temperature and Kappa and Introduction of the Entropy Defect

Olbert’s Kappa Fermi and Bose Distributions

Formation of non-thermal electron velocity distribution functions in kinetic magnetic reconnection

Contact Info

Product

Resources

About