TY - GEN
T1 - From Variational to Bracket Formulations in Nonequilibrium Thermodynamics of Simple Systems
AU - Gay-Balmaz, François
AU - Yoshimura, Hiroaki
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - A variational formulation for nonequilibrium thermodynamics was recently proposed in [7, 8] for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive from a unified perspective several bracket formulations for nonequilibrium thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC brackets are recovered. A similar development has been presented for continuum systems in [6] and applied to multicomponent fluids.
AB - A variational formulation for nonequilibrium thermodynamics was recently proposed in [7, 8] for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible processes. In this paper, we show that this variational formulation yields a constructive and systematic way to derive from a unified perspective several bracket formulations for nonequilibrium thermodynamics proposed earlier in the literature, such as the single generator bracket and the double generator bracket. In the case of a linear relation between the thermodynamic fluxes and the thermodynamic forces, the metriplectic or GENERIC brackets are recovered. A similar development has been presented for continuum systems in [6] and applied to multicomponent fluids.
KW - Bracket formulation
KW - Nonequilibrium thermodynamics
KW - Variational formulation
U2 - 10.1007/978-3-030-26980-7_22
DO - 10.1007/978-3-030-26980-7_22
M3 - Conference contribution
AN - SCOPUS:85077118426
SN - 9783030269791
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 209
EP - 217
BT - Geometric Science of Information - 4th International Conference, GSI 2019, Proceedings
A2 - Nielsen, Frank
A2 - Barbaresco, Frédéric
PB - Springer
T2 - 4th International Conference on Geometric Science of Information, GSI 2019
Y2 - 27 August 2019 through 29 August 2019
ER -