Multiscale heat transport with inertia and thermal vortices

TL;DR

This paper develops a comprehensive Hamiltonian and thermodynamic framework for heat transport, introducing a new phonon hydrodynamics model with vorticity-dependent convective terms, hyperbolic equations, and Galilean invariance, advancing beyond traditional Fourier-based theories.

Contribution

It introduces a novel phonon hydrodynamics model incorporating vorticity effects and hyperbolic, Galilean-invariant equations, linking multiple levels of heat transport description without linearization.

Findings

New phonon hydrodynamics with vorticity-dependent convective terms

Hyperbolic and Galilean-invariant heat transport equations

Vorticity effects cause heat flux to deviate from temperature gradient alignment

Abstract

In this paper, we present a Hamiltonian and thermodynamic theory of heat transport on various levels of description. Transport of heat is formulated within kinetic theory of polarized phonons, kinetic theory of unpolarized phonons, hydrodynamics of polarized phonons, and hydrodynamics of unpolarized phonons. These various levels of description are linked by Poisson reductions, where no linearizations are made. Consequently, we obtain a new phonon hydrodynamics that contains convective terms dependent on vorticity of the heat flux, which are missing in the standard theories of phonon hydrodynamics. Moreover, the equations are hyperbolic and Galilean invariant, unlike current theories for beyond-Fourier heat transport. The vorticity-dependent terms violate the alignment of the heat flux with the temperature gradient even in the stationary state, which is expressed by a Fourier-Crocco equation. The new terms also cause that temperature plays in heat transport a similar role as pressure in aerodynamics.