From variational to bracket formulations in nonequilibrium thermodynamics of simple systems

JOURNAL OF GEOMETRY AND PHYSICS

卷:158

Article

Gay-Balmaz, Francois¹  Yoshimura, Hiroaki² 

[1] Ecole Normale Super, IPSL, LMD, CNRS, 24 Rue Lhomond, F-75005 Paris, France

[2] Waseda Univ, Sch Fundamental Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan

关键词: Nonequilibrium thermodynamics;    Variational formulation;    Bracket formulation;    Metriplectic and GENERIC brackets;   

DOI  :  10.1016/j.geomphys.2020.103812

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free