再论热力学与电磁学的耦合
Revisiting the Coupling of Thermodynamics and Electromagnetics
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中文总结 AI 辅助
本文对比了Dreyer等人的公理化体相热力学电磁耦合理论与Mazur的统计力学路径，推导了守恒定律，发现二者方程结构一致，仅存在微观场涨落的动量贡献差异，明确了电动势强度与洛伦兹磁化的性质及熵函数非对称的成因。
中文摘要 AI 辅助
我们重新研究运动的可极化与可磁化物质中连续介质热力学与电磁理论的耦合问题，遵循两条路径并进行对比。第一条路径是Dreyer、Guhlke和Müller提出的公理化体相理论，其中普适平衡定律通过熵原理闭合。我们证明，内能平衡的源项必须由非对流电流构建，极化电流与洛伦兹磁化通过一个单一恒等式引入，而Dreyer等人并未写出该恒等式，且此恒等式确定了可容许的熵变量以及束缚电流假设的符号。第二条路径是Mazur的统计力学路径，其中宏观麦克斯韦方程通过对含内部电荷载流子的原子系统进行系综平均得到。Mazur在守恒定律前停止推导，因此我们推导了这些守恒定律，并估算了出现的质量修正项的量级。对比表明，在重新定义极化与磁化后，两组方程在结构上一致，唯一不可约的差异是微观场涨落带来的动量贡献，这是纯宏观理论无法复现的。我们进一步证明，电动势强度$\boldsymbol{\textit{E}}$与洛伦兹磁化$\boldsymbol{\textit{M}}$并非建模选择，而是自然出现的，且熵函数的非对称形式是所选能量变量的结果，而非理论缺陷。
英文摘要
We revisit the coupling of continuum thermodynamics and electromagnetic theory for polarisable and magnetisable matter in motion. Two routes are followed and then compared. The first route is the axiomatic bulk theory of Dreyer, Guhlke and Müller, in which universal balance laws are closed by an entropy principle. We show that the source of the internal energy balance must be built with the non-convective electric current, that the polarisation current and the Lorentz magnetisation enter through one single identity, which Dreyer et al.\ do not write down, and that this identity fixes both the admissible entropy variables and the signs of the bound-current ansatz. The second route is the statistical-mechanical one of Mazur, in which the macroscopic Maxwell equations are obtained by ensemble averaging over a system of atoms with internal charge carriers. Mazur stops before the conservation laws, so we derive them, and we estimate the size of the mass-correction terms that appear. The comparison shows that after a redefinition of polarisation and magnetisation the two sets of equations agree structurally. The only irreducible difference is a momentum contribution from microscopic field fluctuations, which can not be reproduced in a purely macroscopic theory. We further show that the electromotive intensity $\mathcal{E}$ and the Lorentz magnetisation $\mathcal{M}$ are not modelling choices but appear by themselves, and that the asymmetric look of the entropy function is a consequence of the chosen energy variable and not a defect of the theory.
