Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction
Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction
复制标题
唯象傅里叶和非傅里叶热传导的数学和信息几何熵
DOI：
10.1103/physreve.96.032131
复制
发表时间：
2017-09-19
影响因子：
2.4
通讯作者：
Cao, Bing-Yang
中科院分区：
文献类型：
--
作者：
Li, Shu-Nan;Cao, Bing-Yang
热力学第二定律决定了热传输的方向，这提供了热力学克劳修斯熵的基本定义。将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框架下的唯象热输运模型中。在这项工作中，熵函数从数学相结合的唯象热传导模型和连接到几个信息几何概念。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，包括热平衡趋势、非平衡指数衰减和渐近性，它们在宏观和微观模型之间架起了一座桥梁。与EIT熵相比，用内能函数表示的数学熵可以避免非傅立叶热传导模型引起的非正局部绝对温度的奇异性。
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.