  The correct modelling 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 work, 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 is recovered as a limiting case, and a "microscopic" definition of
inverse temperature $\beta$ is given. Non-extensivity is not invoked a priori
but enters the picture only through the analysis of correlations between parts
of the system.
