Over the last twenty-five years, the search for generalized equations that allow us to better understand the phenomenon of heat conduction has become an active frontier both in transport theory, and in non-equilibrium thermodynamics, due to the growing interest in nanotechnologies, thermal metamaterials and fast devices. Here we review how some mathematical analogies between generalized heat-transport equations and well-known equations in hydrodynamics, electronics and optics have been helpful to infer new forms of heat transfer arising in extended thermodynamics and to inspire the consideration of new phenomena. We also examine in each case the thermodynamic basis of the respective formulation.

中文翻译：

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扩展热力学中热传递的流体动力学、电子和光学类比

在过去的二十五年里，由于人们对纳米技术、热传导理论的兴趣日益浓厚，对能够让我们更好地理解热传导现象的广义方程的探索已成为输运理论和非平衡热力学的一个活跃前沿领域。超材料和快速设备。在这里，我们回顾了广义传热方程与流体力学、电子学和光学中众所周知的方程之间的一些数学类比如何有助于推断扩展热力学中出现的新传热形式，并激发对新现象的思考。我们还在每种情况下检查各自配方的热力学基础。