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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-10-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/17/10/7213 |
| _version_ | 1798041857765146624 |
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| author | Tatsuaki Wada Hiroshi Matsuzoe Antonio M. Scarfone |
| author_facet | Tatsuaki Wada Hiroshi Matsuzoe Antonio M. Scarfone |
| author_sort | Tatsuaki Wada |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T22:27:26Z |
| format | Article |
| id | doaj.art-6d3d38a3be614038a5325fc7c7b46e4e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:27:26Z |
| publishDate | 2015-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-6d3d38a3be614038a5325fc7c7b46e4e2022-12-22T03:59:36ZengMDPI 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 |
| 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 |
| title | 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_short | Dualistic Hessian Structures Among the Thermodynamic Potentials in the κ-Thermostatistics |
| title_sort | dualistic hessian structures 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 |
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