A non-local and non-linear thermodynamical model of heat transfer at nanoscale beyond the well-known Maxwell–Cattaneo theory is derived. The compatibility of the proposed model with second law of thermodynamics is proved. The model is subsequently used to investigate the propagation of a heat pulse in one-dimensional nanosystems in the linear case. The predicted results are compared with those arising from the Maxwell–Cattaneo theory in order to point out the possible influence both of the non-local effects, and of the relaxation effects of the higher-order fluxes. Some problems related to initial data and boundary conditions are also discussed.

中文翻译：

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超越 Maxwell-Cattaneo 理论的热脉冲传播：应用于一维纳米系统

导出了超越著名的 Maxwell-Cattaneo 理论的纳米尺度传热的非局部和非线性热力学模型。证明了所提出的模型与热力学第二定律的相容性。该模型随后用于研究热脉冲在线性情况下在一维纳米系统中的传播。将预测结果与 Maxwell-Cattaneo 理论产生的结果进行比较，以指出非局部效应和高阶通量弛豫效应的可能影响。还讨论了与初始数据和边界条件相关的一些问题。