Generalized Shannon–Khinchin axioms and uniqueness theorem for pseudo-additive entropies

We consider the Shannon–Khinchin axiomatic systems for the characterization of generalized entropies such as the Sharma–Mittal and Frank–Daffertshofer entropies. We provide the generalization of the Shannon–Khinchin axioms and give the corresponding uniqueness theorem. The previous attempts at such axiomatizations are also discussed. •The generalized Shannon–Khinchin axiomatic systems are considered.•A new class of entropies is derived.•The Sharma–Mittal and Frank–Daffertshofer entropies are derived as a special case.