Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy
Generalization of Shannon-Khinchin axioms to nonextensive systems and the uniqueness theorem for the nonextensive entropy
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DOI：
10.1109/tit.2004.831749
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发表时间：
2004-08
影响因子：
2.5
通讯作者：
H. Suyari
中科院分区：
文献类型：
--
作者：
H. Suyari
Tsallis熵是Shannon熵的单参数推广，是统计物理学中经常讨论的一种新的信息度量。这一新的信息度量在表现出混沌或分维的非扩展系统中提供了许多令人满意的物理解释。我们将广义的Shannon-Khinin公理推广到非扩张系统，并严格地证明了唯一性定理。我们的结果表明，Tsallis熵是所有非扩展熵中最简单的。通过将我们的公理与以前提出的两套公理进行详细的比较，我们揭示了伪可加性作为公理的特殊性。在这种对应中，Tsallis熵作为信息度量的最基本的基础是在信息论框架中建立的。
Tsallis entropy, one-parameter generalization of Shannon entropy, has been often discussed in statistical physics as a new information measure. This new information measure has provided many satisfactory physical interpretations in nonextensive systems exhibiting chaos or fractal. We present the generalized Shannon-Khinchin axioms to nonextensive systems and prove the uniqueness theorem rigorously. Our results show that Tsallis entropy is the simplest among all nonextensive entropies. By the detailed comparisons of our axioms with the previously presented two sets of axioms, we reveal the peculiarity of pseudoadditivity as an axiom. In this correspondence, the most fundamental basis for Tsallis entropy as information measure is established in the information-theoretic framework.