Tsallis相对熵极小化的非延拓三角等式及其它性质
Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization
摘要：
Kullback-Leibler相对熵在涉及由相对熵最小化产生的分布的情况下具有独特的性质。Tsallis相对熵是Kullback-Leibler相对熵在非广延热统计中的单参数推广。本文给出了Tsallis相对熵最小化的一些性质，并与经典情形作了比较。在这样一个最小的相对熵分布的表示，我们强调使用的q-产品，一个运营商，最近推出的数学结构背后的Tsallis统计。我们的主要结果之一是将相对熵最小化的三角等式推广到非广延情形。
英文摘要：
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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