Nonextensive Entropies derived from Form Invariance of Pseudoadditivity

Abstract

The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of Shannon entropy. Information content in a nonextensive system is obtained uniquely from generalized axioms by replacing the usual additivity with pseudoadditivity. The satisfaction of the form invariance of the pseudoadditivity of nonextensive entropy and its information content is found to require the normalization of nonextensive entropies. The proposed principle requires the same normalization as that derived in [A.K. Rajagopal and S. Abe, Phys. Rev. Lett. {\bf 83}, 1711 (1999)], but is simpler and establishes a basis for the systematic definition of various entropies in nonextensive systems.