Derivation of the entropic formula for the statistical mechanics of space plasmas

Kappa distributions describe velocities and energies of plasma populations in space plasmas. The statistical origin of these distributions is associated with the framework of nonextensive statistical mechanics. Indeed, the kappa distribution is derived by maximizing the q entropy of Tsallis, under the constraints of the canonical ensemble. However, the question remains as to what the physical origin of this entropic formulation is. This paper shows that the q entropy can be derived by adapting the additivity of energy and entropy.