标题： 四括号算法用于构建热力学一致的动力学系统 显示英文标题

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

摘要： 提出了一种统一的热力学算法（UTA），用于构建热力学一致的动力学系统，即具有保能而产熵的哈密顿部分和耗散部分的动力学系统。该算法基于Morrison和Updike [Phys. Rev. E 109, 045202 (2024)] 给出的度量泊松4括号。UTA的一个特征是与唯象系数$L^{\alpha\beta}$、哈密顿量$H$和动力学变量$\xi^\beta$相关的力-流关系$\mathbf{J}^\alpha = - L^{\alpha\beta}\, \nabla(\delta H / \delta \xi^\beta)$。该算法被应用于Navier-Stokes-Fourier系统、Cahn-Hilliard-Navier-Stokes系统以及Brenner-Navier-Stokes-Fourier系统，并获得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.