Art

J-GLOBAL ID：201902256598174067   Reference number：19A0915244

Information Geometry of κ-Exponential Families: Dually-Flat, Hessian and Legendre Structures

κ指数族の情報幾何学:双対平坦,HessianおよびLegendre構造【JST・京大機械翻訳】

Author (3)： Scarfone Antonio M. (Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche (ISC-CNR), c/o Politecnico di Torino, 10129 Torino, Italy) ,  Matsuzoe Hiroshi (Department of Computer Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan) ,  Wada Tatsuaki (Region of Electrical and Electronic Systems Engineering, Ibaraki University, Nakanarusawa-cho, Hitachi 316-8511, Japan)
Material： Entropy (Web)
Volume： 20  Issue： 6  Page： 436  Publication year： 2018 
JST Material Number： U7179A  ISSN： 1099-4300  Document type： Article
Article type： 文献レビュー  Country of issue： Switzerland (CHE)  Language： ENGLISH (EN)

Abstract/Point： In this paper, we present a re...

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Thesaurus term： manifold(mathematics) ,  thermodynamics ,  *geometry ,  curvature ,  inner product ,  statistical mechanics ,  invariance
Semi thesaurus term： *情報幾何 , 【Automatic Indexing@JST】

Author keywords (6)： κ-generalized statistical mechanics ,  information geometry ,  dually-flat geometry ,  Hessian geometry ,  Legendre structure ,  divergence functions

JST classification (1)： Quantum optics in general  (BD04010X)

Reference (81)：

• Amari, S.-I.; Nagaoka, H. Methods of Information Geometry; American Mathematical Society: Providence, RI, USA, 2000.
• Amari, S.-I. Information Geometry and Its Applications; Springer: Tokyo, Japan, 2016.
• Gibbs, J.W. A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces. Trans. Conn. Acad. 1873, II, 382-404.
• Charathéodory, C. Untersuchungen über die Grundlagen der Thermodynamik. Math. Ann. 1909, 67, 355-386. (In German)
• Ruppeiner, G. Riemannian geometry in thermodynamic fluctuation theory. Rev. Mod. Phys. 1995, 67, 605-659.

Terms in the title (3)： 指数 ,  情報幾何学 ,  平坦