TY - GEN

T1 - Dirac Structures and Variational Formulation of Thermodynamics for Open Systems

AU - Yoshimura, Hiroaki

AU - Gay-Balmaz, François

N1 - Funding Information:
Acknowledgements. H.Y. is partially supported by JSPS Grant-in-Aid for Scientific Research (17H01097), JST CREST Grant Number JPMJCR1914, the MEXT Top Global University Project, Waseda University (SR 2020C-194) and the Organization for University Research Initiatives (Evolution and application of energy conversion theory in collaboration with modern mathematics). F.G.B. is partially supported by the ANR project GEOMFLUID, ANR-14-CE23-0002-01.
Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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U2 - 10.1007/978-3-030-77957-3_12

DO - 10.1007/978-3-030-77957-3_12

M3 - Conference contribution

AN - SCOPUS:85112640841

SN - 9783030779566

T3 - Springer Proceedings in Mathematics and Statistics

SP - 221

EP - 246

BT - Geometric Structures of Statistical Physics, Information Geometry, and Learning - SPIGL’20

A2 - Barbaresco, Frédéric

A2 - Nielsen, Frank

PB - Springer

T2 - Workshop on Joint Structures and Common Foundations of Statistical Physics, Information Geometry and Inference for Learning, SPIGL 2020

Y2 - 27 July 2020 through 31 July 2020

ER -