TY - GEN
T1 - Dirac Structures in Thermodynamics of Non-simple Systems
AU - Yoshimura, Hiroaki
AU - Gay-Balmaz, François
N1 - Funding Information:
H.Yoshimura 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 2021C-134) and the Organization for University Research Initiatives (Evolution and application of energy conversion theory in collaboration with modern mathematics).
Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - We present the Dirac structures and the associated Dirac system formulations for non-simple thermodynamic systems by focusing upon the cases that include irreversible processes due to friction and heat conduction. These systems are called non-simple since they involve several entropy variables. We review the variational formulation of the evolution equations of such non-simple systems. Then, based on this, we clarify that there exists a Dirac structure on the Pontryagin bundle over a thermodynamic configuration space and we develop the Dirac dynamical formulation of such non-simple systems. The approach is illustrated with the example of an adiabatic piston.
AB - We present the Dirac structures and the associated Dirac system formulations for non-simple thermodynamic systems by focusing upon the cases that include irreversible processes due to friction and heat conduction. These systems are called non-simple since they involve several entropy variables. We review the variational formulation of the evolution equations of such non-simple systems. Then, based on this, we clarify that there exists a Dirac structure on the Pontryagin bundle over a thermodynamic configuration space and we develop the Dirac dynamical formulation of such non-simple systems. The approach is illustrated with the example of an adiabatic piston.
KW - Adiabatic piston
KW - Dirac structures
KW - Non-simple systems
KW - Thermodynamics
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U2 - 10.1007/978-3-030-80209-7_98
DO - 10.1007/978-3-030-80209-7_98
M3 - Conference contribution
AN - SCOPUS:85112545769
SN - 9783030802080
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 918
EP - 925
BT - Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frédéric
PB - Springer Science and Business Media Deutschland GmbH
T2 - 5th International Conference on Geometric Science of Information, GSI 2021
Y2 - 21 July 2021 through 23 July 2021
ER -