Physical correlations lead to kappa distributions

TL;DR

This paper demonstrates that the thermodynamics of particle correlations in space plasmas inherently lead to the formation of kappa velocity distributions, linking physical correlations with specific statistical behaviors.

Contribution

It establishes for the first time that physical correlations among particles necessarily imply the existence of kappa distributions in space plasma thermodynamics.

Findings

Physical correlations are consistent only with kappa distributions.

Derivation of velocity distribution functions using the entropic defect concept.

Reveals the foundational role of correlations in plasma velocity 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.