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 conservation of energy, describes the distribution of temperature over space and time.

Typically, the heat equation is assumed to be the end of the story for thermal conduction. However, the macroscopic theory leaves some fundamental questions unanswered. For example, why is diamond an exceptional thermal conductor, whereas gallium arsenide, a material with the same crystal structure, is only an average one? Lattice vibrations have long been understood as being responsible for heat...

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