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Nonlinear diffusion equations for maximum entropy principle with kappa-entropy

Research Project

Project/Area Number 19540391
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionIbaraki University

Principal Investigator

WADA Tatsuaki  Ibaraki University, 工学部, 准教授 (00240549)

Research Collaborator SCARFONE Antonio maria  トリノ工科大学, 物理学科, 准教授
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsκエントロピ / エントロピ最大原理 / 非線型拡散方程式 / Fokker-Planck方程式 / リアプノフ汎関数 / ダイバージェンス / 統計力学 / リアプノブ汎関数 / 自己相似性
Research Abstract

This work is a research study on the kappa-generalized thermostatistics based on kappa-entropy, which was proposed in 2002 by Dr. G.Kaniadakis and Dr. A.M.Scarfone in Politechnical University in Torino (Politecnico di Torino), Italy. We have found that the explicit expressions of the nonlinear diffusion and Fokker-Planck equations associated with kappa-entropy, and shown the underlying mechanism of the generalized maximum entropy (MaxEnt) principle for kappa-entropy.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (41 results)

All 2010 2009 2008 2007 Other

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (19 results) Remarks (8 results)

  • [Journal Article] Information geometry of q-Gaussian densities and behaviors of solutions to related diffusion equations2010

    • Author(s)
      A. Ohara, T. Wada
    • Journal Title

      J.Phys.A : Math.Theor. 43

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Information geometry of q-Gaussian densities and behaviors of solutions to related diffusion equations2010

    • Author(s)
      A.Ohara, T.Wada
    • Journal Title

      J.Phys.A : Math.Theor. 43

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized log-likelihood functions and Bregman divergences2009

    • Author(s)
      T. Wada
    • Journal Title

      J.Math.Phys. 50

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A nonlinear drift which leads to κ-generalized distributions2009

    • Author(s)
      T. Wada
    • Journal Title

      Eur.Phys.J.B 73

      Pages: 287-291

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lie symmetries and related group-invariant solutions of a nonlinear Fokker-Planck equation based on the Sharma-Taneja-Mittal entropy2009

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

      Brazilian J.Phys. 39

      Pages: 478-485

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics2009

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

      The European Physical Journal B 70

      Pages: 65-71

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gauss' law of error revisited in the framework of Sharma-Taneja-Mittal information measure2009

    • Author(s)
      A. M. Scarfone, H. Suyari, T. Wada
    • Journal Title

      Central European Journal of Physics 7

      Pages: 414-420

    • Related Report
      2009 Final Research Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics2009

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

      Euro.Phys.J.B 70

      Pages: 65-71

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized log-likelihood functions and Bregman divergences2009

    • Author(s)
      T.Wada
    • Journal Title

      J.Math.Phys. 50

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A nonlinear drift which leads to κ-generalized distributions2009

    • Author(s)
      T.Wada
    • Journal Title

      Eur.Phys.J.B 73

      Pages: 287-291

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics2009

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

      The European Physical Journal B 70

      Pages: 6571-6571

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the non-linear Fokker-Planck equation associated with κ-entropy2007

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

      AIP Conference Proceedings 965

      Pages: 177-180

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A two-parameter generalization of Shannon-Khinchin axioms and the uniqueness theorem2007

    • Author(s)
      T. Wada and H. Suyari
    • Journal Title

      Physics Letter A 368

      Pages: 199-205

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the non-linear Fokker-Planck equation associated with κ-entropy2007

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

      AIP Conference Proceedings 965

      Pages: 177-180

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Finite difference and averaging operators in generalized entropies2009

    • Author(s)
      T. Wada, A. M. Scarfone
    • Organizer
      京都大学数理解析研究所 (RIMS) 国際ワークショップ「Mathematical Aspects of Generalized Entropies and their Applications」Kyoto
    • Place of Presentation
      京都テルサ
    • Year and Date
      2009-07-07
    • Related Report
      2009 Final Research Report
  • [Presentation] Finite difference and averaging operators in generalized entropies2009

    • Author(s)
      T.Wada, A.M.Scarfone
    • Organizer
      京都大学数理解析研究所(RIMS)国際ワークショップ「Mathematical Aspects of Generalized Entropies and their Applications」Kyoto, July 7-9(2009)
    • Place of Presentation
      京都テルサ
    • Year and Date
      2009-07-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] κ-Gauss 分布を定常状態とする非線型ドリフト2009

    • Author(s)
      和田達明
    • Organizer
      日本物理学会第64回年次大会
    • Place of Presentation
      立教学院池袋キャンパス
    • Year and Date
      2009-03-30
    • Related Report
      2009 Final Research Report
  • [Presentation] κ-Gauss分布を定常状態とする非線型ドリフト2009

    • Author(s)
      和田達明
    • Organizer
      日本物理学会第64回年次大会30aPS-72
    • Place of Presentation
      立教学院池袋キャンパス
    • Year and Date
      2009-03-30
    • Related Report
      2008 Annual Research Report
  • [Presentation] A nonlinear drift which leads to κ-generalized distributions in Gauss' law of error2009

    • Author(s)
      T. Wada
    • Organizer
      Application of Physics in Financial Analysis 7-th International ; Conference
    • Place of Presentation
      東工大大岡山キャンパス
    • Related Report
      2008 Annual Research Report
  • [Presentation] A generalization of the log-likelihood function and weighted average in Gauss' law of error2008

    • Author(s)
      T. Wada, H. Suyari
    • Organizer
      International Symposium on Information Theory and its Application, ISITA2008
    • Place of Presentation
      Langharn Hotel, Auckland, New Zealand
    • Year and Date
      2008-12-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] κ-エントロピに関する非線型拡散方程式2008

    • Author(s)
      和田達明
    • Organizer
      日本物理学会2008年秋季大会
    • Place of Presentation
      岩手大学
    • Year and Date
      2008-09-23
    • Related Report
      2009 Final Research Report
  • [Presentation] Gauss' law of error revisited in the framework of Sharma-Taneja-Mittal informatio measure2008

    • Author(s)
      A.M. Scarfone, H. Suyari, T. Wada
    • Organizer
      International Conference in Statistical Physics, (SigmaPhi2008)
    • Place of Presentation
      Orthodox Academy of Crete, Greece
    • Year and Date
      2008-09-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] κ-エントロピーに関する非線型拡散方程式2008

    • Author(s)
      和田達明
    • Organizer
      日本物理学会2008年秋季大会23aPS-72
    • Place of Presentation
      岩手大学
    • Year and Date
      2008-09-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] Asymptotic solutions of a nonlinear diffusive equation in the framework of κ-generalized statistical mechanics2008

    • Author(s)
      T. Wada, A. M. Scarfone
    • Organizer
      International Conference in Statistical Physics, (SigmaPhi2008)
    • Place of Presentation
      Orthodox Academy of Crete, Greece
    • Year and Date
      2008-07-17
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] Generalized log-likelihood functions and Bregman divergences2008

    • Author(s)
      T. Wada
    • Organizer
      International Conference in Statistical Physics, (SigmaPhi2008)
    • Place of Presentation
      Orthodox Academy of Crete, Greece
    • Year and Date
      2008-07-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] Gauss の誤差法則と Hyperensembles2008

    • Author(s)
      和田達明
    • Organizer
      日本物理学会第63回年次大会
    • Place of Presentation
      近畿大学理工学部
    • Year and Date
      2008-03-25
    • Related Report
      2009 Final Research Report
  • [Presentation] Gaussの誤差法則とHyperensembles2008

    • Author(s)
      和田 達明
    • Organizer
      日本物理学会第63回年次大会
    • Place of Presentation
      近畿大学理工学部
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] 一般化熱統計学における Legendre 構造 : 非線形 Fokker-Planck 方程式における Bregman divergence との関連2007

    • Author(s)
      和田達明
    • Organizer
      RIMS研究集会「非可換解析とミクロ・マクロ双対性」
    • Place of Presentation
      京都大学数理解析研究所 (RIMS)
    • Year and Date
      2007-10-15
    • Related Report
      2009 Final Research Report
  • [Presentation] 一般化熱統計学におけるLegendre構造:非線形Fokker-Planck方程式におけるBregman divergenceとの関連2007

    • Author(s)
      和田 達明
    • Organizer
      RIMS研究集会「非可換解析とミクロ・マクロ双対性」
    • Place of Presentation
      京都大学数理解析研究所(RIMS)
    • Year and Date
      2007-10-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] 非線型 Fokker-Planck 方程式の自己相似解の漸近挙動と一般化エントロピー最大原理2007

    • Author(s)
      和田達明
    • Organizer
      日本物理学会第62回年次大会
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-09-21
    • Related Report
      2009 Final Research Report
  • [Presentation] 非線型Fokker-Planck方程式の自己相似解の漸近挙動と一般化エントロピー最大原理2007

    • Author(s)
      和田 達明
    • Organizer
      日本物理学会第62回年次大会
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-09-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the non-linear Fokker-Planck equation associated with κ-entropy2007

    • Author(s)
      T. Wada
    • Organizer
      International Conference on Complexity, Metastability and Nonextensivity, (CT-NEXT07)
    • Place of Presentation
      Catania University, Italy
    • Year and Date
      2007-07-04
    • Related Report
      2009 Final Research Report
  • [Presentation] On the non-linear Fokker-Planck equation associated with κ-entropy2007

    • Author(s)
      T. Wada
    • Organizer
      Intemational Conference on Complexity Metastability and Nonextensivity, (CT-NEXTO7)
    • Place of Presentation
      Catania University, Italy
    • Year and Date
      2007-07-04
    • Related Report
      2007 Annual Research Report
  • [Remarks] ホームページ等, 茨城大学研究者情報総覧

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2009 Final Research Report
  • [Remarks] 個人ホームページ

    • URL

      http://www.ipc.ibaraki.ac.jp/~wada

    • Related Report
      2009 Final Research Report
  • [Remarks] 茨城大学研究者情報総覧

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2009 Annual Research Report
  • [Remarks] 個人ホームページ

    • URL

      http://www.ipc.ibaraki.ac.jp/~wada

    • Related Report
      2009 Annual Research Report
  • [Remarks] 茨城大学研究者情報総覧

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2008 Annual Research Report
  • [Remarks] 個人ホームページ

    • URL

      http://www.ipc.ibaraki.ac.jp/~wada

    • Related Report
      2008 Annual Research Report
  • [Remarks] 茨城大学研究者情報総覧

    • URL

      http://info.ibaraki.ac.jp/scripts/websearch/index.htm

    • Related Report
      2007 Annual Research Report
  • [Remarks] 個人ホームページ

    • URL

      http://www.ipc.ibaraki.ac.jp/~wada

    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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