A two-parameter generalization of Shannon-Khinchin axioms and the uniqueness theorem

Based on the one-parameter generalization of Shannon-Khinchin (SK) axioms presented by one of the authors, and utilizing a tree-graphical representation, we have developed for the first time a two-parameter generalization of the SK axioms in accordance with the two-parameter entropy introduced by Sharma, Taneja, and Mittal. The corresponding unique theorem is also proved. It is found that our two-parameter generalization of Shannon additivity is a natural consequence from the Leibniz product rule of the two-parameter Chakrabarti-Jagannathan difference operator.