The Fourier heat conduction as a strong kinetic effect

TL;DR

This paper demonstrates that in certain one-dimensional systems, kinetic effects can dominate over hydrodynamic effects, leading to normal Fourier heat conduction, contrary to the common belief that hydrodynamics causes its breakdown.

Contribution

The study analytically and numerically shows that kinetic effects can lead to Fourier heat conduction in 1D systems, challenging the prevailing hydrodynamic perspective.

Findings

Kinetic effects can dominate heat conduction in 1D systems.

The HCAF exhibits a fast decay followed by a slow tail.

Fourier law validity depends on the dominance of the kinetic stage.

Abstract

For an one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law. Usually the HCAF undergoes a fast decaying kinetic stage followed by a long, slowly decaying hydrodynamic tail. In a finite range of the system size, we find that whether the system follows the Fourier law depends on whether the kinetic stage dominates. Our study is illustrated by the 1D diatomic gas model, with which the HCAF is derived analytically and verified numerically by molecular dynamics simulations.