TY - GEN
T1 - Hamiltonian Variational Formulation for Non-simple Thermodynamic Systems
AU - Yoshimura, Hiroaki
AU - Gay-Balmaz, François
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - A Lagrangian variational formulation for nonequilibrium thermodynamics was proposed in [2–4]. In this paper, we develop a Hamiltonian analogue of the Lagrangian variational formulation for non-simple thermodynamic systems [6, 8]. We start with the Lagrangian variational formulation for simple systems, where the Lagrangian is degenerate. Under some assumption, we show how to construct the Hamiltonian variational formulation for nonequilibrium thermodynamics for the simple case. Then, we extend it to the case of adiabatically closed non-simple systems, in which there exists several entropy variables in addition to the mechanical variables. Finally, we illustrate our theory of the Hamiltonian variational formulation by an example of the adiabatic piston problem.
AB - A Lagrangian variational formulation for nonequilibrium thermodynamics was proposed in [2–4]. In this paper, we develop a Hamiltonian analogue of the Lagrangian variational formulation for non-simple thermodynamic systems [6, 8]. We start with the Lagrangian variational formulation for simple systems, where the Lagrangian is degenerate. Under some assumption, we show how to construct the Hamiltonian variational formulation for nonequilibrium thermodynamics for the simple case. Then, we extend it to the case of adiabatically closed non-simple systems, in which there exists several entropy variables in addition to the mechanical variables. Finally, we illustrate our theory of the Hamiltonian variational formulation by an example of the adiabatic piston problem.
KW - Hamiltonian variational formulation
KW - Non-simple systems
KW - Nonequilibrium thermodynamics
KW - degenerate Lagrangians
UR - https://www.scopus.com/pages/publications/85173522072
U2 - 10.1007/978-3-031-38299-4_24
DO - 10.1007/978-3-031-38299-4_24
M3 - Conference contribution
AN - SCOPUS:85173522072
SN - 9783031382987
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 221
EP - 230
BT - Geometric Science of Information - 6th International Conference, GSI 2023, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frédéric
PB - Springer Science and Business Media Deutschland GmbH
T2 - The 6th International Conference on Geometric Science of Information, GSI 2023
Y2 - 30 August 2023 through 1 September 2023
ER -