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Open AccessArticle

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