Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-ThermostatisticsReport as inadecuate




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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





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Academic Editor: George Ruppeiner

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





Author: Tatsuaki Wada 1,* , Hiroshi Matsuzoe 2 and Antonio M. Scarfone 3

Source: http://mdpi.com/



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