Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
Phys Rev E. 2017 Sep;96(3-1):032131. doi: 10.1103/PhysRevE.96.032131. Epub 2017 Sep 19.
The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.
热力学第二定律支配着热传输的方向，为热力学克劳修斯熵提供了基本定义。熵的定义进一步推广到经典不可逆热力学和扩展不可逆热力学（EIT）框架下的唯象热传输模型中。在这项工作中，来自数学的熵函数与唯象热传导模型相结合，并与几个信息几何概念联系起来。这些数学熵的长时间行为在唯象热传导中表现出广泛的多样性和物理图像，包括趋向热平衡和非平衡的指数衰减以及渐近行为，这些行为在宏观和微观建模之间架起了桥梁。与 EIT 熵不同的是，用内能函数表示的数学熵可以避免非傅里叶热传导模型引起的与非负局部绝对温度相关的奇点。
