Non-equilibrium statistical mechanical approach to the formation of non-Maxwellian electron distribution in space

Abstract

Boltzmann-Gibbs (BG) entropy has additive and extensive properties, but for certain physical systems, such as those governed by long-range interactions – plasma or fully ionized gas being an example – it is speculated that the entropy must be non-additive and non-extensive. Because of the fact that Tsallis entropy possesses such characteristics, many spacecraft observations of charged particle distributions in space are interpreted with the conceptual framework based upon Tsallis statistical principles. This paper formulates the non-equilibrium statistical theory of space plasma, and it is shown that the steady state electrostatic turbulence in plasma coincides with the formation of non-Maxwellian electron distribution function known as the kappa distribution. The kappa distribution is equivalent to the q-Gaussian distribution in the Tsallis statistical theory, which represents the most probable state subject to Tsallis entropy. This finding represents an independent confirmation that the space plasma may indeed be governed by the Tsallis statistical principle.