Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s law and its various extensions—the Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys type, Ginzburg–Landau (Allen–Cahn) type and ballistic–diffusive heat conduction equations—are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.

中文翻译：

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使用内部变量和 GENERIC 的非傅立叶热传导案例研究

同时应用具有内部变量的非平衡热力学方法（NET-IV）和非平衡可逆-不可逆耦合的通用方程框架（GENERIC），我们证明，在热传导理论中，熵电流乘数可以是解释为松弛状态变量。傅立叶定律及其各种扩展——Maxwell-Cattaneo-Vernotte、Guyer-Krumhansl、Jeffreys 型、Ginzburg-Landau (Allen-Cahn) 型和弹道-扩散热传导方程——在这两种公式中都得到了推导。沿着这些思路，还进行了 NET-IV 和 GENERIC 的比较。我们的结果可能为超越傅里叶热传导的微观/多尺度理解铺平道路，并为热传导问题的数值模拟开辟新途径。