Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics

We explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort ex...

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Main Authors:	Tatsuaki Wada, Hiroshi Matsuzoe, Antonio M. Scarfone
Format:	Article
Language:	English
Published:	MDPI AG 2015-10-01
Series:	Entropy
Subjects:	κ-entropy κ-exponential κ-logarithm information geometry Hessian geometry dually-flat thermodynamic geometry
Online Access:	http://www.mdpi.com/1099-4300/17/10/7213

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spelling	doaj-6d3d38a3be614038a5325fc7c7b46e4e2020-11-24T22:08:13ZengMDPI AGEntropy1099-43002015-10-0117107213722910.3390/e17107213e17107213Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-ThermostatisticsTatsuaki Wada0Hiroshi Matsuzoe1Antonio M. Scarfone2Department of Electrical and Electronic Engineering, Ibaraki University, Nakanarusawacho, Hitachi 316-8511, JapanDepartment of Computer Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokisocho, Nagoya 466-8555, JapanIstituto dei Sistemi Complessi (ISC-CNR) c/o Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino I-10129, ItalyWe explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort expectations and the other with the standard expectations. The associated κ-generalized metrics are derived and related to the κ-generalized fluctuation-response relations among the thermodynamic potentials in the κ-thermostatistics.http://www.mdpi.com/1099-4300/17/10/7213κ-entropyκ-exponentialκ-logarithminformation geometryHessian geometrydually-flatthermodynamic geometry
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tatsuaki Wada Hiroshi Matsuzoe Antonio M. Scarfone
spellingShingle	Tatsuaki Wada Hiroshi Matsuzoe Antonio M. Scarfone Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics Entropy κ-entropy κ-exponential κ-logarithm information geometry Hessian geometry dually-flat thermodynamic geometry
author_facet	Tatsuaki Wada Hiroshi Matsuzoe Antonio M. Scarfone
author_sort	Tatsuaki Wada
title	Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics
title_short	Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics
title_full	Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics
title_fullStr	Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics
title_full_unstemmed	Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics
title_sort	dualistic hessian structures among the thermodynamic potentials in the κ-thermostatistics
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2015-10-01
description	We explore the information geometric structures among the thermodynamic potentials in the κ-thermostatistics, which is a generalized thermostatistics based on the κ-deformed entropy. We show that there exists two different kinds of dualistic Hessian structures: one is associated with the κ-escort expectations and the other with the standard expectations. The associated κ-generalized metrics are derived and related to the κ-generalized fluctuation-response relations among the thermodynamic potentials in the κ-thermostatistics.
topic	κ-entropy κ-exponential κ-logarithm information geometry Hessian geometry dually-flat thermodynamic geometry
url	http://www.mdpi.com/1099-4300/17/10/7213
work_keys_str_mv	AT tatsuakiwada dualistichessianstructuresamongthethermodynamicpotentialsinthekthermostatistics AT hiroshimatsuzoe dualistichessianstructuresamongthethermodynamicpotentialsinthekthermostatistics AT antoniomscarfone dualistichessianstructuresamongthethermodynamicpotentialsinthekthermostatistics
_version_	1725817160187510784

Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics

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