Foundations of Statistical Mechanics in Space Plasmas

Abstract:

Systems at thermal equilibrium have their distribution function of particle velocities stabilized into a Maxwell distribution, which is connected with the classical framework of Boltzmann-Gibbs (BG) statistical mechanics. However, Maxwell distributions are rare in space plasmas; the vast majority of these plasmas reside at stationary states out of thermal equilibrium, which are described by kappa distributions. Kappa distributions do not embody BG statistics, but instead, they are connected with the generalized statistical framework of non-extensive statistical mechanics that offers a solid theoretical basis for describing particle systems like collisionless space plasmas. Through the statistical formulation of kappa distributions, basic thermodynamic variables like the temperature, thermal pressure, and entropy, become physically meaningful and determinable, similarly to their classical BG description at thermal equilibrium. In addition, useful formulations of kappa distributions were developed in order to describe multi-particle distributions, and particle systems with a non-zero potential energy. Finally, the variety of kappa distribution formulations and the proven tools of non-extensive statistical mechanics have been successfully applied to a numerous space plasmas throughout the heliosphere, from the inner heliosphere (e.g., the solar wind and planetary magnetospheres) to the outer heliosphere (e.g., the inner heliosheath) and beyond.