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

Entropy

Tatsuaki Wada³  Hiroshi Matsuzoe¹  Antonio M. Scarfone² 

[1] Department of Computer Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokisocho, Nagoya 466-8555, Japan; E-Mail:;Istituto dei Sistemi Complessi (ISC-CNR) c/o Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino I-10129, Italy; E-Mail:;Department of Electrical and Electronic Engineering, Ibaraki University, Nakanarusawacho, Hitachi 316-8511, Japan

关键词: κ-entropy;    κ-exponential;    κ-logarithm;    information geometry;    Hessian geometry;    dually-flat;    thermodynamic geometry;   

DOI  :  10.3390/e17107213

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.