How to properly describe continuum thermodynamics of binary mixtures where each constituent has its own momentum? The Symmetric Hyperbolic Thermodynamically Consistent (SHTC) framework and Hamiltonian mechanics in the form of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provide two answers, which are similar but not identical, and are compared in this article. They are compared both analytically and numerically on several levels of description, varying in the amount of detail. Namely, a reduction to a more common one-momentum setting is shown, where the effects of the second momentum translate into diffusive fluxes. Both SHTC and GENERIC can thus be interpreted as a method specifying diffusive flux in standard theory. The GENERIC equations, stemming from the Liouville equation, contain terms expressing self-advection of the relative velocity by itself, which lead to a vorticity-dependent diffusion matrix after the reduction. The SHTC equations, on the other hand, do not contain such terms. We also discuss the possibility to formulate a theory of mixtures with two momenta and only one temperature that is compatible with the Liouville equation and possesses the Hamiltonian structure, including Jacobi identity.

如何正确描述每种成分都有自己动量的二元混合物的连续热力学？对称双曲热力学一致 (SHTC) 框架和非平衡可逆-不可逆耦合通用方程 (GENERIC) 形式的哈密顿力学提供了两个相似但不相同的答案，本文对此进行了比较。它们在多个描述层面上进行了分析和数字比较，细节程度各不相同。即，显示了到更常见的单动量设置的减少，其中第二动量的影响转化为扩散通量。因此，SHTC 和 GENERIC 都可以解释为标准理论中指定扩散通量的方法。源于刘维尔方程的 GENERIC 方程包含表示相对速度本身的自平流的项，这在简化后产生了依赖于涡度的扩散矩阵。另一方面，SHTC 方程不包含此类项。我们还讨论了建立具有两个动量和只有一个温度的混合物理论的可能性，该理论与刘维尔方程兼容并具有哈密顿结构，包括雅可比恒等式。