TY - GEN
T1 - Dirac Structures and Variational Formulation of Thermodynamics for Open Systems
AU - Yoshimura, Hiroaki
AU - Gay-Balmaz, François
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2021/1/1
Y1 - 2021/1/1
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.
UR - https://www.scopus.com/pages/publications/85112640841
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 -