Diffusion of heat, energy, momentum, and mass in one-dimensional systems

TL;DR

This study investigates how heat, energy, momentum, and mass diffuse in one-dimensional systems, revealing linear relationships and challenging previous assumptions about heat and energy diffusion.

Contribution

It demonstrates that diffusion of heat and momentum can be expressed as linear combinations of energy and mass diffusion, providing new insights into hydrodynamic modes.

Findings

Diffusion of energy and mass can be expressed as linear combinations of heat and momentum.

The dynamic structure factor may not reliably probe all diffusion processes.

Heat diffusion can differ qualitatively from energy diffusion.

Abstract

We study diffusion processes of local fluctuations of heat, energy, momentum, and mass in three paradigmatic one-dimensional systems. For each system, diffusion processes of four physical quantities are simulated and the cross correlations between them are investigated. We find that, in all three systems, diffusion processes of energy and mass can be perfectly expressed as a linear combination of those of heat and momentum, suggesting that diffusion processes of heat and momentum may represent the heat mode and the sound mode in the hydrodynamic theory. In addition, the dynamic structure factor, which describes the diffusion behavior of local mass density fluctuations, is in general insufficient for probing diffusion processes of other quantities because in some cases there is no correlation between them. We also find that the diffusion behavior of heat can be qualitatively different from that of energy, and, as a result, previous studies trying to relate heat conduction to energy diffusion should be revisited.