Three classes of nonextensive entropies characterized by Shannon   additivity and pseudoadditivity
  Nonextensive entropies are divided into three classes, each of which is characterized by Shannon additivity and pseudoadditivity. One of the three classes has properties of both additivities. The remaining classes have only one property of the two additivities, respectively. An example of nonextensive entropy is shown concretely for each class. In particular, one class is found to consist of only the Tsallis entropy. More precisely, the Tsallis entropy is proved to be uniquely determined by only these two additivities. The present classification using these two distinct additivities reveals unique characteristics of the Tsallis entropy. 
Hiroki Suyari