The uniequness theorem for the Tsallis entropy by introducing the generalized Faddeev’s axiom is proven. Our result improves the recent result, the uniqueness theorem for Tsallis entropy by the generalized Shannon-Khinchin’s axiom in [7], in the sence that our axiom is simpler than his one, as similar that Faddeev’s axiom is simpler than Shannon-Khinchin’s one.

The uniqueness theorem for the relative entropy was proven by A.Hobson. Recently, the Tsallis entropy was characterized by H.Suyari in terms of the generalized ShannonKhinchin’s axiom. In this short paper, we characterize the Tsallis relative entropy in the finite discrete system by generalizing the conditions in Hobson’s axiom.

Maximum entropy principles in nonextensive statistical physics are revisited as an application of the Tsallis relative entropy defined for non-negative matrices in the framework of matrix analysis. In addition, some matrix trace inequalities related to the Tsallis relative entropy are studied.

We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes’ inequality.

ISSN: 2186-1390 http://www.ijcvsp.com Abstract In this paper, a fuzzy approach for image segmentation based on Tsallis entropy is introduced. This approach employs fuzzy Tsallis entropy to measure the structural information of image and to locate the optimal threshold desired by segmentation. The proposed method draws upon the postulation that the optimal threshold concurs with maximum informat...

Entropy is a key measure in studies related to information theory and its many applications. Campbell of the first time recognized that exponential of Shannon’s entropy is just the size of the sample space when the distribution is uniform. In this paper, we introduce a quantity which is called exponential Tsallis-Havrda-Charvat entropy and discuss its some properties. Further, we gave the appli...

Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. One-parameter extensions for Shannon entropy have been studied by many researchers. The Rényi entropy [2] and the Tsallis entropy [3] are famous. In the paper [4], the uniqueness theorem for the Tsallis entropy was proved. Also, in our...

Over the last couple of decades nonextensive Tsallis entropy has shown remarkable applicability to describe nonequilibrium physical systems with large variability and multifractal structure. Herein, we review recent results from the application of Tsallis statistical mechanics to the detection of dynamical changes related with the occurrence of magnetic storms. We extend our review to describe ...