Information theoretical properties of Tsallis entropies
Information theoretical properties of Tsallis entropies
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DOI：
10.1063/1.2165744
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发表时间：
2006-02-01
影响因子：
1.3
通讯作者：
Furuichi, S
中科院分区：
文献类型：
--
作者：
Furuichi, S
由Daroczy导出了非加性熵之一的β型熵的链式法则和次可加性。本文进一步研究了典型的非加性熵Tsallis型熵之间的关系。将链式法则推广到Tsallis相对熵和非加性熵。我们给出了一些与Tsallis熵有关的不等式，特别是Tsallis型熵的强次可加性和非可加性熵的次可加性。由次可加性和强次可加性自然分别定义了Tsallis互熵和Tsallis条件互熵，然后我们再次给出了Tsallis互熵的链式规则。我们用萨利斯熵给出熵距的性质。最后给出了基于信息论的参数化推广结果。(c) 2006年美国物理研究所。
A chain rule and a subadditivity for the entropy of type beta, which is one of the nonadditive entropies, were derived by Daroczy. In this paper, we study the further relations among Tsallis type entropies which are typical nonadditive entropies. The chain rule is generalized by showing it for Tsallis relative entropy and the nonadditive entropy. We show some inequalities related to Tsallis entropies, especially the strong subadditivity for Tsallis type entropies and the subadditivity for the nonadditive entropies. The subadditivity and the strong subadditivity naturally lead to define Tsallis mutual entropy and Tsallis conditional mutual entropy, respectively, and then we show again chain rules for Tsallis mutual entropies. We give properties of entropic distances in terms of Tsallis entropies. Finally we show parametrically extended results based on information theory. (c) 2006 American Institute of Physics.