Physical Correlations Lead to Kappa Distributions

Abstract

The recently developed concept of “entropic defect” is important for understanding the foundations of thermodynamics in space plasma physics, and more generally for systems with physical correlations among their particles. Using this concept, this paper derives the basic formulation of the distribution function of velocities (or kinetic energies) in space plasma particle populations. Earlier analyses have shown how the formulation of kappa distributions is interwoven with the presence of correlations among the particles’ velocities. This paper shows, for the first time, that the reverse is true: the thermodynamics of particles’ physical correlations are consistent only with the existence of kappa distributions.

Non-linear diffusive shock acceleration: A recipe for injection of electrons

“…In the next section, we shall use semi-analytical Blasi's model of nonlinear DSA [10,11] to obtain non-thermal spectra of both protons and electrons, starting from their quasi-thermal spectra for which we assumed the κ-distribution, a commonly observed distribution in out-of-equilibrium space plasmas [21][22][23][24].…”

Complexity of Recent Earthquake Swarms in Greece in Terms of Non-Extensive Statistical Physics

“…According to this property and for two probabilistic independent events A and B , the total entropy Sq of the system A + B satisfies: This property is known as pseudo-additivity and is further distinguished into super-additivity if q < 1, sub-additivity if q > 1 and additivity when q = 1 (Boltzmann–Gibbs statistics) where the last term on the right-hand side of Equation (2) vanishes, and the additivity property is recovered. This has been recently discussed in terms of the entropy defect [ 48 ].…”

Extensive entropy: the case of zero entropy defect

“…(2) Thermodynamic relationship -Connection with BG entropy The Sackur-Tetrode equation is the expression of entropy in terms of temperature T [31,32]; the dependence on other thermodynamic parameters and constants can be enclosed in the involved thermal constant T 0 , so that the entropy depends on the ratio T/T 0 . Then, T 0 constitutes the lowest temperature for the entropy to be positive [27,28,33,34].…”

“…The paper focuses on the origin of this relationship and its connection with thermodynamics, using the concept of entropy defect, that is, the decrease in a system's entropy caused by the presence of long-range correlations among its constituents [18,[27][28][29]; in the absence of correlations, the entropy becomes extensive and expressed by the BG formulation. The paper is organized as follows.…”