$Information Geometry on the $\kappa$-Thermostatistics$

Information Geometry on the $\kappa$-Thermostatistics

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...

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Main Authors:	Tatsuaki Wada, Antonio M. Scarfone
Format:	Article
Language:	English
Published:	MDPI AG 2015-03-01
Series:	Entropy
Subjects:	$\kappa$-entropy $\kappa$-exponential $\kappa$-logarithm information geometry Fisher metric dually-flat fluctuation-response relation
Online Access:	http://www.mdpi.com/1099-4300/17/3/1204

id	doaj-3bb1fd81f8384c7c88fb4bf047444a60
record_format	Article
spelling	doaj-3bb1fd81f8384c7c88fb4bf047444a602020-11-24T21:39:27ZengMDPI AGEntropy1099-43002015-03-011731204121710.3390/e17031204e17031204Information Geometry on the $\kappa$-ThermostatisticsTatsuaki Wada0Antonio M. Scarfone1Department of Electrical and Electronic Engineering, Ibaraki University, Hitachi, Ibaraki, 316-8511, JapanIstituto dei Sistemi Complessi (ISC-CNR) c/o Politecnico di Torino, Corso Duca degli Abruzzi 24,I-10129 Torino, ItalyWe 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.http://www.mdpi.com/1099-4300/17/3/1204$\kappa$-entropy$\kappa$-exponential$\kappa$-logarithminformation geometryFisher metricdually-flatfluctuation-response relation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tatsuaki Wada Antonio M. Scarfone
spellingShingle	Tatsuaki Wada Antonio M. Scarfone Information Geometry on the $\kappa$-Thermostatistics Entropy $\kappa$-entropy $\kappa$-exponential $\kappa$-logarithm information geometry Fisher metric dually-flat fluctuation-response relation
author_facet	Tatsuaki Wada Antonio M. Scarfone
author_sort	Tatsuaki Wada
title	Information Geometry on the $\kappa$-Thermostatistics
title_short	Information Geometry on the $\kappa$-Thermostatistics
title_full	Information Geometry on the $\kappa$-Thermostatistics
title_fullStr	Information Geometry on the $\kappa$-Thermostatistics
title_full_unstemmed	Information Geometry on the $\kappa$-Thermostatistics
title_sort	information geometry on the $\kappa$-thermostatistics
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2015-03-01
description	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.
topic	$\kappa$-entropy $\kappa$-exponential $\kappa$-logarithm information geometry Fisher metric dually-flat fluctuation-response relation
url	http://www.mdpi.com/1099-4300/17/3/1204
work_keys_str_mv	AT tatsuakiwada informationgeometryonthekappathermostatistics AT antoniomscarfone informationgeometryonthekappathermostatistics
_version_	1725931426425077760

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

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