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Entropy 2015, 17(10), 7213-7229; doi:10.3390/e17107213

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

1
Department of Electrical and Electronic Engineering, Ibaraki University, Nakanarusawacho, Hitachi 316-8511, Japan
2
Department of Computer Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokisocho, Nagoya 466-8555, Japan
3
Istituto dei Sistemi Complessi (ISC-CNR) c/o Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino I-10129, Italy
*
Author to whom correspondence should be addressed.
Academic Editor: George Ruppeiner
Received: 28 July 2015 / Revised: 29 September 2015 / Accepted: 15 October 2015 / Published: 22 October 2015
(This article belongs to the Special Issue Geometry in Thermodynamics)
View Full-Text   |   Download PDF [260 KB, uploaded 22 October 2015]

Abstract

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. View Full-Text
Keywords: κ-entropy; κ-exponential; κ-logarithm; information geometry; Hessian geometry; dually-flat; thermodynamic geometry κ-entropy; κ-exponential; κ-logarithm; information geometry; Hessian geometry; dually-flat; thermodynamic geometry
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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MDPI and ACS Style

Wada, T.; Matsuzoe, H.; Scarfone, A.M. Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics. Entropy 2015, 17, 7213-7229.

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