Extended entropies and disorder
Extended entropies and disorder
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DOI：
10.1142/s0219525905000373
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发表时间：
2005-03-01
影响因子：
0.4
通讯作者：
Shiner, JS
中科院分区：
文献类型：
--
作者：
Davison, M;Shiner, JS
兰兹伯格的无序概念，即标准化为最大熵的熵，最初是为香农信息论熵提出的，以克服熵作为无序度量的基于广延性的缺陷。我们将兰茨伯格的概念概括为三类扩展熵：Renyi、Tsallis 和 Landsberg-Vedral。我们展示了仁义紊乱与称为多重分形的维度谱之间的密切联系。处理了三个例子，包括一个用于幂律分布的例子和一个基于逻辑图的例子。在这三个例子的基础上，证明了需要所有三类扩展无序来充分表征系统的相应属性。我们推测，并草拟了一个证明来支持，所有三种扩展的无序也足以完全确定维度谱。
Landsberg's notion of disorder, entropy normalized to maximum entropy, was originally proposed for the Shannon information-theoretic entropy to overcome extensivity-based deficiencies of entropy as a measure of disorder. We generalize Landsberg's concept to three classes of extended entropies: Renyi, Tsallis and Landsberg-Vedral. We show an intimate connection between the Renyi disorders and the spectrum of dimensions known as multifractals. Three examples are treated, including one for power law distributions and one based on the logistic map. On the basis of the three examples, it is demonstrated that all three classes of extended disorder are required to fully characterize the corresponding properties of a system. We conjecture, and sketch a proof to support, that all three extended disorders are also sufficient to completely determine a dimension spectrum.