TY - GEN
T1 - Dirac structures in nonequilbrium thermodynamics
AU - Yoshimura, Hiroaki
AU - Gay-Balmaz, François
N1 - Funding Information:
Acknowledgements. F.G.B. is partially supported by the ANR project GEOM-
Funding Information:
FLUID, ANR-14-CE23-0002-01; H.Y. is partially supported by JSPS Grant-in-Aid for Scientific Research (26400408, 16KT0024, 24224004), Waseda University Grant for Special Research Project (2017K-167), and the MEXT “Top Global University Project”.
Publisher Copyright:
© 2017, Springer International Publishing AG.
PY - 2017
Y1 - 2017
N2 - In this paper, we show that the evolution equations for nonequilibrium thermodynamics can be formulated in terms of Dirac structures on the Pontryagin bundle P =TQ ⊕ T*Q, where Q = Q ×s R denotes the thermodynamic configuration manifold. In particular, we extend the use of Dirac structures from the case of linear nonholonomic constraints to the case of nonlinear nonholonomic constraints. Such a nonlinear constraint comes from the entropy production associated with irreversible processes in nonequilibrium thermodynamics. We also develop the induced Dirac structure on N=T*Q × R and the associated Lagrange-Dirac and Hamilton-Dirac dynamical formulations.
AB - In this paper, we show that the evolution equations for nonequilibrium thermodynamics can be formulated in terms of Dirac structures on the Pontryagin bundle P =TQ ⊕ T*Q, where Q = Q ×s R denotes the thermodynamic configuration manifold. In particular, we extend the use of Dirac structures from the case of linear nonholonomic constraints to the case of nonlinear nonholonomic constraints. Such a nonlinear constraint comes from the entropy production associated with irreversible processes in nonequilibrium thermodynamics. We also develop the induced Dirac structure on N=T*Q × R and the associated Lagrange-Dirac and Hamilton-Dirac dynamical formulations.
KW - Dirac structures
KW - Implicit systems
KW - Irreversible processes
KW - Nonequilibrium thermodynamics
KW - Nonlinear constraints
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U2 - 10.1007/978-3-319-68445-1_48
DO - 10.1007/978-3-319-68445-1_48
M3 - Conference contribution
AN - SCOPUS:85033723035
SN - 9783319684444
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 410
EP - 417
BT - Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frederic
A2 - Nielsen, Frank
PB - Springer Verlag
T2 - 3rd International Conference on Geometric Science of Information, GSI 2017
Y2 - 7 November 2017 through 9 November 2017
ER -