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Information Geometry on the \(\kappa\)-Thermostatistics

Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan
Istituto dei Sistemi Complessi (ISC-CNR) c/o Politecnico di Torino, Corso Duca degli Abruzzi 24,I-10129 Torino, Italy
Author to whom correspondence should be addressed.
Academic Editor: Giorgio Kaniadakis
Entropy 2015, 17(3), 1204-1217;
Received: 3 February 2015 / Revised: 5 March 2015 / Accepted: 9 March 2015 / Published: 12 March 2015
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
We explore the information geometric structure of the statistical manifold generated by the \(\kappa\)-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 \(\kappa\)-formalism based on the \(\kappa\)-generalized exponential family. View Full-Text
Keywords: \(\kappa\)-entropy; \(\kappa\)-exponential; \(\kappa\)-logarithm; information geometry; Fisher metric; dually-flat; fluctuation-response relation \(\kappa\)-entropy; \(\kappa\)-exponential; \(\kappa\)-logarithm; information geometry; Fisher metric; dually-flat; fluctuation-response relation
MDPI and ACS Style

Wada, T.; Scarfone, A.M. Information Geometry on the \(\kappa\)-Thermostatistics. Entropy 2015, 17, 1204-1217.

AMA Style

Wada T, Scarfone AM. Information Geometry on the \(\kappa\)-Thermostatistics. Entropy. 2015; 17(3):1204-1217.

Chicago/Turabian Style

Wada, Tatsuaki, and Antonio M. Scarfone 2015. "Information Geometry on the \(\kappa\)-Thermostatistics" Entropy 17, no. 3: 1204-1217.

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