Heat under the microscope

[Introduction] Recent advances in computational and spectroscopic tools offer new insights into the nature of thermal conduction at ever-finer length scales and ways to control it. Heat conduction is familiar to us all and yet requires a wide range of physics—statistical mechanics, crystallography, and quantum mechanics among them—to fully explain. At the macroscale, heat conduction can be described as a diffusion process in which energy moves along a temperature gradient. The heat flux dissipated by the gradient depends on a material property, the thermal conductivity, as described by the constitutive relation, Fourier’s law. The heat equation, which is derived from Fourier’s law and the c…