On certain incomplete statistics

The foundations of the incomplete statistics recently proposed by Wang is rediscussed in the context of the canonical statistical ensemble. It is found that the incomplete normalization condition, ∑pqi=1 (i=1,…,w), where pi is the probability of a given microstate, is not compatible with the entropic non-extensive formula proposed by Tsallis. It is proved that the entropic function proposed by Wang must be written as Sq=−kB∑pi2q−1lnqpi, whereas the form proposed by Tsallis namely, Sq=−kB∑piqlnqpi, is directly associated with the standard normalization condition (∑ipi=1).