Legendre structure of κ-thermostatistics revisited in the framework of information geometry
Legendre structure of κ-thermostatistics revisited in the framework of information geometry
复制标题
在信息几何框架下重新审视κ-恒温统计的勒让德结构
DOI：
10.1088/1751-8113/47/27/275002
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
T. Wada
中科院分区：
文献类型：
--
作者：
A. M. Scarfone;T. Wada
信息几何是应用微分几何工具研究概率分布族或统计模型的有力框架。它通过用赋予黎曼度量的可微流形来识别概率分布空间，为推导概率论中的许多重要结构提供了一个有用的框架。在这篇文章中，我们在信息几何的框架下，重新讨论了基于熵的κ-κ热力学的几个方面。在引入与κ分布相关的对偶平坦结构之后，我们证明了在信息几何的形式中得到的对偶势对应于表征Φκ变形统计力学的勒让德结构的广义马西厄函数κ和广义熵Sκ。此外，我们还得到了与进一步发展理论相关的几个量，如护航分布和典范散度。
Information geometry is a powerful framework in which to study families of probability distributions or statistical models by applying differential geometric tools. It provides a useful framework for deriving many important structures in probability theory by identifying the space of probability distributions with a differentiable manifold endowed with a Riemannian metric. In this paper, we revisit some aspects concerning the κ-thermostatistics based on the entropy Sκ in the framework of information geometry. After introducing the dually flat structure associated with the κ-distribution, we show that the dual potentials derived in the formalism of information geometry correspond to the generalized Massieu function Φκ and the generalized entropy Sκ characterizing the Legendre structure of the κ-deformed statistical mechanics. In addition, we obtain several quantities, such as escort distributions and canonical divergence, relevant for the further development of the theory.
影响因子：
2.6
作者：
Ohara, Atsumi
通讯作者：
Ohara, Atsumi
DOI：
--
发表时间：
2006
期刊：
Progress of Theoretical Physics Supplement 162
影响因子：
--
作者：
T.Wada;A.M.Scarfone
通讯作者：
A.M.Scarfone
基于 Sharma-Taneja-Mittal 的非线性 Fokker-Planck 方程的李对称性和相关群不变解
影响因子：
1.6
作者：
A. M. Scarf one;T. Wada
通讯作者：
T. Wada