Colissionless plasmas are non-extensive systems which, due to the long-range interaction between their components, are incapable of reaching thermal equilibrium, even in a steady state. These systems cannot, therefore, be described statistically by a single canonical distribution with well-defined inverse temperature β = 1/kBT and are commonly described via two alternative approaches: namely Tsallis statistics and Superstatistics. The use of Superstatistics in describing steady-state plasmas has been proposed by several authors, more recently Ourabah et al. In this work we study the consequences of this assumption of Superstatistics for steady-state plasmas. We explicitly show that only the ensembles characterized by the condition P(x|ρ) = ρ(H(x)) are consistent with a generalized definition of temperature introduced recently. We show how this formalism is employed in the case of plasma, considering …