Abstract Phonon hydrodynamics uses the fields of the total energy and the heat flux as state variables. We extend it by promoting the microscopic internal energy field into the status of an extra independent state variable. The governing equations of both the phonon and the extended (two temperature) phonon hydrodynamics are formulated as particular realizations of the abstract GENERIC equation. Such unified formulation makes both theories manifestly compatible with mechanics and thermodynamics. Also differences and similarities (in the physical content, in the mathematical structure, and in qualitative properties of solutions) between the two heat transfer theories, as well as their mutual compatibility, become manifestly displayed.

中文翻译：

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声子流体动力学的二次温度扩展

摘要 声子流体动力学以总能量场和热通量场作为状态变量。我们通过将微观内部能量场提升为额外独立状态变量的状态来扩展它。声子和扩展（两个温度）声子流体动力学的控制方程被公式化为抽象 GENERIC 方程的特定实现。这种统一的表述使这两种理论与力学和热力学明显兼容。两种传热理论之间的异同（物理内容、数学结构和解的定性性质）以及它们的相互兼容性也得到了明显的体现。