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.

中文翻译：

---

从简单系统的非平衡热力学中的变分公式到括号公式

最近在 [7, 8] 中为离散和连续系统提出了非平衡热力学的变分公式。这个公式将经典力学的哈密顿原理扩展到包括不可逆过程。在本文中，我们展示了这种变分公式产生了一种建设性和系统的方法，可以从统一的角度推导出文献中早期提出的非平衡热力学的几个支架公式，例如单发电机支架和双发电机支架。在热力学通量和热力学力之间呈线性关系的情况下，可恢复 metriplectic 或 GENERIC 支架。[6] 中为连续系统提出了类似的发展，并应用于多组分流体。