Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization |
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Institution: | 1. Decision Sciences Group, Indian Institute of Management, Lucknow, India;2. Production and Quantitative Methods Area, Indian Institute of Management, Ahmedabad, India;1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi''an 710072, PR China;2. College of Science, Huazhong Agricultural University, Wuhan 430070, PR China |
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Abstract: | Kullback–Leibler relative-entropy has unique properties in cases involving distributions resulting from relative-entropy minimization. Tsallis relative-entropy is a one-parameter generalization of Kullback–Leibler relative-entropy in the nonextensive thermostatistics. In this paper, we present the properties of Tsallis relative-entropy minimization and present some differences with the classical case. In the representation of such a minimum relative-entropy distribution, we highlight the use of the q-product, an operator that has been recently introduced to derive the mathematical structure behind the Tsallis statistics. One of our main results is the generalization of triangle equality of relative-entropy minimization to the nonextensive case. |
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