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The information geometric structures on the kappa-generalized thermostatistics

Research Project

Project/Area Number 25400188
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionIbaraki University

Principal Investigator

Wada Tatsuaki  茨城大学, 工学部, 教授 (00240549)

Research Collaborator Scarfone Antonio M.  トリノ工科大学, 応用科学工学科, 准教授
Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Keywordsκ-指数型分布 / 情報幾何 / κ-エントロピ- / ダイバージェンス / 双対平坦 / 揺動応答関係 / κ-エントロピ / フィーシャー情報計量 / κ-統計力学 / エスコート期待値 / 一般化エントロピー / κエントロピー / フィッシャー情報計量 / 情報幾何学
Outline of Final Research Achievements

We found the conjugate representations for constructing the statistical manifold associated with a family of the kappa-generalized exponential distributions. We have obtained the explicit expressions of the kappa-generalized geometrical quantities (e.g, Fisher metric, affine connections, divergence functions) which characterize the information geometric structures. We also showed that the kappa-statistical manifold is dually flat, which is an important feature in information geometry.
From these results we derive a kappa-generalization of the fluctuation-response relations, and pointed out the importance of an escort expectation value in addition to the conventional linear expectation.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (18 results)

All 2015 2014 2013 Other

All Int'l Joint Research (1 results) Journal Article (4 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 4 results,  Open Access: 3 results,  Acknowledgement Compliant: 3 results) Presentation (6 results) (of which Invited: 3 results) Remarks (7 results)

  • [Int'l Joint Research] イタリア学術会議 複雑系研究所(ISC-CNR)/トリノ工科大学(イタリア)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Deformed Algebras and Generalizations of Independence on Deformed Exponential Families2015

    • Author(s)
      Hiroshi Matsuzoe, Tatsuaki Wada
    • Journal Title

      Entropy

      Volume: 17 Issue: 8 Pages: 5729-5751

    • DOI

      10.3390/e17085729

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Dualistic Hessian Structures Among the Thermodynamic Potentials in the k-Thermostatistics2015

    • Author(s)
      Tatsuaki Wada, Hiroshi Matsuzoe, Antonio M. Scarfone
    • Journal Title

      Entropy

      Volume: 17 Issue: 10 Pages: 7213-7229

    • DOI

      10.3390/e17107213

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Information geometry on the \kappa-thermostatistics2015

    • Author(s)
      T. Wada and A.M. Scarfone
    • Journal Title

      Entropy

      Volume: 17 Issue: 3 Pages: 1204-1217

    • DOI

      10.3390/e17031204

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] The \kappa-generalizations of stirling approximation and multinominal coefficients2013

    • Author(s)
      Tatsuaki Wada, Hiroki Suyari
    • Journal Title

      Entropy

      Volume: 15 Issue: 12 Pages: 5144-5153

    • DOI

      10.3390/e15125144

    • Related Report
      2014 Research-status Report 2013 Research-status Report
    • Peer Reviewed
  • [Presentation] 熱力学 ⇔ 情報幾何2015

    • Author(s)
      和田 達明
    • Organizer
      ミニワークショップ 統計多様体の幾何学とその周辺 (7)
    • Place of Presentation
      北海道大学理学部 4号館501
    • Year and Date
      2015-09-01
    • Related Report
      2015 Annual Research Report
  • [Presentation] κ変形指数分布に基づく情報幾何構造2015

    • Author(s)
      和田達明、Antonio M. Scarfone
    • Organizer
      日本物理学会
    • Place of Presentation
      早稲田大学早稲田キャンパス
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] 異常拡散を示す離散時間量子ウォーク2014

    • Author(s)
      和田達明、鹿野豊
    • Organizer
      京都大学数理解析研究所共同研究 「統計多様体の諸分野への応用」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-11-19 – 2014-11-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Information geometry on the κ-thermostatistics2014

    • Author(s)
      Tatsuaki Wada and Antonio M. Scarfone
    • Organizer
      International conference on statistical physics ΣΦ2014
    • Place of Presentation
      ギリシャ、ロードス島
    • Year and Date
      2014-07-07 – 2014-07-11
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 一般化エントロピーに基づく統計力学と情報幾何構造2014

    • Author(s)
      和田 達明
    • Organizer
      ミニワークショップ 統計多様体の幾何学とその周辺 (5)
    • Place of Presentation
      北海道大学理学部 4号館501
    • Related Report
      2013 Research-status Report
  • [Presentation] 一般化エントロピーに基づく統計力学の拡張とその情報幾何構造2014

    • Author(s)
      和田 達明
    • Organizer
      京都大学数理解析研究所短期共同研究 「統計多様体の幾何学の新展開 」
    • Place of Presentation
      京都大学数理解析研究所 110室
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks] 茨城大学研究者情報総覧

    • URL

      http://info.ibaraki.ac.jp/Profiles/4/0000304/profile.html

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
  • [Remarks] ResearchGate

    • URL

      http://www.researchgate.net/profile/Tatsuaki.Wada

    • Related Report
      2015 Annual Research Report
  • [Remarks] ReserchGate

    • URL

      http://www.reserchgate.net/profile/Tatsuaki_Wada

    • Related Report
      2014 Research-status Report
  • [Remarks] Wada's Home Page

    • URL

      http://9tempo.ee.ibaraki.ac.jp

    • Related Report
      2014 Research-status Report
  • [Remarks] 茨城大学 研究者情報総覧

    • URL

      http://info.ibaraki.ac.jp/Profiles/4/0000304/profile.html

    • Related Report
      2013 Research-status Report
  • [Remarks] ResearchGate

    • URL

      http://www.researchgate.net/profile/Tatsuaki_Wada

    • Related Report
      2013 Research-status Report
  • [Remarks] Wada's Home Page

    • URL

      http://9tempo.ee.ibaraki.ac.jp/

    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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