Abstract
A non-Markovian partial differential equation, rooted in the theory of Brownian motion, is proposed for describing heat conduction by phonons. Although a finite speed of propagation is a built-in feature of the equation, it does not give rise to an inauthentic wave front that results from the application of Cattaneo's equation. Even a simplified, analytically tractable version of the equation yields results close to those found by solving, through more elaborate means, the equation of phonon radiative transfer.
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