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Entropy 2015, 17(3), 1204-1217; doi:10.3390/e17031204

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

1
Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, Japan
2
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
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)
View Full-Text   |   Download PDF [241 KB, uploaded 12 March 2015]

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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

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