Deformed statistics formulation of the information bottleneck method
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Tsallis differential entropy and divergences derived from the generalized Shannon-Khinchin axioms
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
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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.