标题： 用于构建热力学一致动力系统的时间乘子4括号算法 显示英文标题

标题： Metriplectic 4-bracket algorithm for constructing thermodynamically consistent dynamical systems

摘要： 一种统一的热力学算法（UTA）用于构建热力学一致的动力系统，即具有保守能量同时产生熵的哈密顿和耗散部分的系统。 该算法基于Morrison和Updike [Phys. Rev. E 109, 045202 (2024)]中给出的度量-泊松4括号。 UTA的一个特点是力-通量关系$\mathbf{J}^\alpha = - L^{\alpha\beta}\, \nabla(\delta H / \delta \xi^\beta)$，用于现象学系数$L^{\alpha\beta}$、哈密顿量$H$和动力变量$\xi^\beta$。 该算法被应用于纳维-斯托克斯-傅里叶、Cahn-Hilliard-纳维-斯托克斯以及Brenner-纳维-斯托克斯-傅里叶系统，并得到了这些系统的显著推广。 显示英文摘要

摘要： A unified thermodynamic algorithm (UTA) is presented for constructing thermodynamically consistent dynamical systems, i.e., systems that have Hamiltonian and dissipative parts that conserve energy while producing entropy. The algorithm is based on the metriplectic 4-bracket given in Morrison and Updike [Phys.\ Rev.\ E 109, 045202 (2024)]. A feature of the UTA is the force-flux relation $\mathbf{J}^\alpha = - L^{\alpha\beta}\, \nabla(\delta H / \delta \xi^\beta)$ for phenomenological coefficients $L^{\alpha\beta}$, Hamiltonian $H$ and dynamical variables $\xi^\beta$. The algorithm is applied to the Navier-Stokes-Fourier, the Cahn-Hilliard-Navier-Stokes, and and Brenner-Navier-Stokes-Fourier systems, and significant generalizations of these systems are obtained.