Tsallis熵合成与海森堡群
Tsallis entropy composition and the Heisenberg group
摘要：
我们提出了一个嵌入的Tsallis熵到3维海森堡群，为了理解广义独立编码的Tsallis熵组成属性的含义。我们推断，Tsallis熵组成诱导分形性质的基础上的欧氏空间。使用Milnor/Wolf/Tits/Gromov定理，我们证明了为什么Tsallis熵描述的系统的基本配置/相空间对于离散和黎曼情况都具有多项式增长。我们提供了一个几何框架，阐明安倍晋三的公式Tsallis熵，在潘苏衍生的子黎曼空间之间的映射。
英文摘要：
We present an embedding of the Tsallis entropy into the 3-dimensional Heisenberg group, in order to understand the meaning of generalized independence as encoded in the Tsallis entropy composition property. We infer that the Tsallis entropy composition induces fractal properties on the underlying Euclidean space. Using a theorem of Milnor/Wolf/Tits/Gromov, we justify why the underlying configuration/phase space of systems described by the Tsallis entropy has polynomial growth for both discrete and Riemannian cases. We provide a geometric framework that elucidates Abe's formula for the Tsallis entropy, in terms the Pansu derivative of a map between sub-Riemannian spaces.
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