Nonextensive Statistical Mechanics

218 6 Generalizing Nonextensive Statistical MechanicsIn Eq. (6.41), E ∗ stands for the lowest admissible energy for the system and a isa Lagrange multiplier. Using Eqs. (6.41) and (6.30) we can in principle get the QSFF(κ) for a given temperature distribution function f (β ′ ). Thus, in principle at least,the various superstatistics can be accommodated into spectral statistics. However,there are certain cases where spectral statistics can go further than superstatistics.For example, it appears that through superstatistics we can, up to now, only producethe nonadditive entropies S q for q ≥ 1, while in the spectral formalism we can havethem for arbitrary values of q. This is the reason for which we have written the lastlogical inclusion in structure (6.6) as it stands there.