Generalization of Shannon–Khinchin Axioms to Nonextensive Systems and the Uniqueness Theorem for the Nonextensive Entropy

Abstract

Tsallis entropy, one-parameter generalization of Shannon entropy, has been often discussed in statistical physics as a new information measure. This new information measure has provided many satisfactory physical interpretations in nonextensive systems exhibiting chaos or fractal. We present the generalized Shannon-Khinchin axioms to nonextensive systems and prove the uniqueness theorem rigorously. Our results show that Tsallis entropy is the simplest among all nonextensive entropies. By the detailed comparisons of our axioms with the previously presented two sets of axioms, we reveal the peculiarity of pseudoadditivity as an axiom. In this correspondence, the most fundamental basis for Tsallis entropy as information measure is established in the information-theoretic framework.