A new equation for describing heat conduction by phonons

TL;DR

This paper introduces a novel heat conduction equation based on Brownian motion theory that accurately models phonon heat transfer with finite propagation speed, avoiding unphysical wave fronts seen in traditional hyperbolic models.

Contribution

It presents a new equation for phonon heat conduction rooted in Brownian motion, offering a more realistic finite speed propagation without artificial wave fronts.

Findings

Equation closely matches phonon radiative transfer results

Simplified form yields analytically tractable solutions

Provides a unified paradigm for Brownian motion and radiative transfer

Abstract

A new equation, rooted in the theory of Brownian motion, is proposed for describing heat conduction by phonons. Though 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 the hyperbolic heat equation (of Cattaneo). 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. An explanation is given as to why both Brownian motion and its inverse (radiative transfer) provide equally serviceable paradigms for phonon-mediated heat conduction.