Single-particle velocity distributions of collisionless, steady-state plasmas must follow superstatistics.

The correct modeling of velocity distribution functions for particles in steady-state plasmas is a central element in the study of nuclear fusion and also in the description of space plasmas. In this paper, a statistical mechanical formalism for the description of collisionless plasmas in a steady state is presented, based solely on the application of the rules of probability and not relying on the concept of entropy. Beck and Cohen's superstatistical framework [Beck and Cohen, Physica A 322, 267 (2003)PHYADX0378-437110.1016/S0378-4371(03)00019-0] is recovered as a limiting case, and a "microscopic" definition of inverse temperature β is given. Nonextensivity is not invoked a priori but enters the picture only through the analysis of correlations between parts of the system.