The thermal conduction across material interfaces is studied using a generalized Langevin equation (gLE) theory. A general statistical formula of thermal interfacial conductance (TIC) is derived at the slow fluctuation limit in terms of the time auto-correlation functions of interfacial heat current (QACF) ⟨q(t)q(0)⟩ and the heat capacity C_V. At the bulk limit of $C_{\mathrm{V}}\to \infty$, this general TIC formula reduces to the previously proposed Green–Kubo type of TIC formula. Beyond the bulk limit, the TIC of a material with finite C_V can be calculated using the first and second moments of the interfacial QACF. These statistical TIC formulas provide the basis to adopt equilibrium molecular dynamics simulations to calculate the TIC of real material interfaces beyond the bulk limit, including the interfaces at the nanoscale. The TIC of two types of non-Markov model interfaces with analytic forms of QACF is predicted by the reported gLE theory, and the results of these non-Markov interfaces are compared with those of a Markov interface.

中文翻译：

---

跨材料界面热传导的广义朗之万方程理论

使用广义朗之万方程 (gLE) 理论研究跨材料界面的热传导。根据界面热流(QACF) ⟨ q ( t ) q (0)⟩和热容C _V的时间自相关函数，推导出了在缓慢波动极限下的界面热导率(TIC)的一般统计公式. 在批量限制$C_{\mathrm{伏}}\to \infty$，这个通用的 TIC 公式简化为之前提出的 Green-Kubo 类型的 TIC 公式。超出体积限制，可以使用界面 QACF 的一阶和二阶矩计算具有有限C _V的材料的 TIC 。这些统计 TIC 公式为采用平衡分子动力学模拟计算超出体积限制的真实材料界面的 TIC（包括纳米级界面）提供了基础。两种类型的非马尔可夫模型接口与 QACF 的解析形式的 TIC 是通过报告的 gLE 理论预测的，并将这些非马尔可夫接口的结果与马尔可夫接口的结果进行比较。