From variational to bracket formulations in nonequilibrium thermodynamics of simple systems

François Gay-Balmaz*, Hiroaki Yoshimura

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

A variational formulation for nonequilibrium thermodynamics was recently proposed in Gay-Balmaz and Yoshimura (2017a, 2017b) 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 bracket is recovered. We also show how the processes of reduction by symmetry can be applied to these brackets. In the reduced setting, we also consider the case in which the coadjoint orbits are preserved and explain the link with double bracket dissipation. A similar development has been presented for continuum systems in Eldred and Gay-Balmaz (2020) and applied to multicomponent fluids.

本文言語English
論文番号103812
ジャーナルJournal of Geometry and Physics
158
DOI
出版ステータスPublished - 2020 12月

ASJC Scopus subject areas

  • 数理物理学
  • 物理学および天文学(全般)
  • 幾何学とトポロジー

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