Generalization of Shannon-Khinchin Axioms to Nonextensive Systems and   the Uniqueness Theorem
  The Shannon-Khinchin axioms are generalized to nonextensive systems and the uniqueness theorem for the nonextensive entropy is proved rigorously. In the present axioms, Shannon additivity is used as additivity in contrast to pseudoadditivity in Abe's axioms. The results reveal that Tsallis entropy is the simplest among all nonextensive entropies which can be obtained from the generalized Shannon-Khinchin axioms. 
Hiroki Suyari