Multiscale Modeling &Simulation, Volume 19, Issue 1, Page 533-549, January 2021.
We present a first-principle based approach that leads from a many-particle description to a nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at the nano-mechanical scale. By enforcing statistical consistency, in that the statistics of local energy is consistent with that from an all-atom description, we identify the driving force as well as the model parameters in these generalized constitutive models. The connections to established generalized constitutive relations, including Cattaneo--Vernotte-type models, will be demonstrated.

中文翻译：

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纳米级热传导的非线性本构模型

多尺度建模与仿真，第 19 卷，第 1 期，第 533-549 页，2021 年 1 月
。纳米机械尺度。通过加强统计一致性，因为局部能量的统计与全原子描述的一致，我们确定了这些广义本构模型中的驱动力和模型参数。将展示与已建立的广义本构关系的联系，包括 Cattaneo--Vernotte 型模型。