Dirac Structures and Variational Formulation of Thermodynamics for Open Systems

Hiroaki Yoshimura*, François Gay-Balmaz

*この研究の対応する著者

研究成果: Conference contribution

抄録

In this paper, we make a review of our recent development of Dirac structures and the associated variational formulation for nonequilibrium thermodynamics (see, [15, 16]). We specifically focus on the case of simple and open systems, in which the thermodynamic state is represented by one single entropy and the transfer of matter and heat with the exterior is included. We clarify the geometric structure by introducing an induced Dirac structure on the covariant Pontryagin bundle and then develop the associated dynamical system (the port-Dirac systems) in the context of time-dependent nonholonomic systems with nonlinear constraints of thermodynamic type. We also present the variational structure associated with the Dirac formulation in the context of the generalized Lagrange-d’Alembert-Pontryagin principle.

本文言語English
ホスト出版物のタイトルGeometric Structures of Statistical Physics, Information Geometry, and Learning - SPIGL’20
編集者Frédéric Barbaresco, Frank Nielsen
出版社Springer
ページ221-246
ページ数26
ISBN(印刷版)9783030779566
DOI
出版ステータスPublished - 2021
イベントWorkshop on Joint Structures and Common Foundations of Statistical Physics, Information Geometry and Inference for Learning, SPIGL 2020 - Les Houches, France
継続期間: 2020 7 272020 7 31

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
361
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

Conference

ConferenceWorkshop on Joint Structures and Common Foundations of Statistical Physics, Information Geometry and Inference for Learning, SPIGL 2020
国/地域France
CityLes Houches
Period20/7/2720/7/31

ASJC Scopus subject areas

  • 数学 (全般)

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