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Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization

Ambedkar Dukkipati·M. Narasimha Murty·Shalabh Bhatnagar
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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 generalization of triangle equality of relative-entropy minimization to the nonextensive case.

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Ambedkar Dukkipati, M. Narasimha Murty, Shalabh Bhatnagar. 2005-03-22. Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization. https://doi.org/10.1016/j.physa.2005.06.072

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