Information Geometry on the κ-Thermostatistics

Entropy

Tatsuaki Wada²  Antonio M. Scarfone¹ 

[1] Istituto dei Sistemi Complessi (ISC-CNR) c/o Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; E-Mail:;Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan

关键词: κ-entropy;    κ-exponential;    κ-logarithm;    information geometry;    Fisher metric;    dually-flat;    fluctuation-response relation;   

DOI  :  10.3390/e17031204

来源: mdpi

【 摘 要 】

We explore the information geometric structure of the statistical manifold generated by the κ-deformed exponential family. The dually-flat manifold is obtained as a dualistic Hessian structure by introducing suitable generalization of the Fisher metric and affine connections. As a byproduct, we obtain the fluctuation-response relations in the κ-formalism based on the κ-generalized exponential family.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland