Abstract
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.
F. Gay-Balmaz is partially supported by the ANR project GEOMFLUID, ANR-14-CE23-0002-01; H. Yoshimura is partially supported by JSPS Grant-in-Aid for Scientific Research (S) 24224004, the MEXT Top Global University Project and Waseda University (SR 2019C-176).
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Gay-Balmaz, F., Yoshimura, H. (2019). From Variational to Bracket Formulations in Nonequilibrium Thermodynamics of Simple Systems. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2019. Lecture Notes in Computer Science(), vol 11712. Springer, Cham. https://doi.org/10.1007/978-3-030-26980-7_22
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