Connection between heat diffusion and heat conduction in one-dimensional systems

TL;DR

This paper investigates the relationship between heat diffusion and heat conduction in one-dimensional systems, revealing that they are not generally connected, and highlights potential misconceptions when using particle indices as spatial variables.

Contribution

The study clarifies the distinction between energy diffusion and heat conduction in 1D systems and introduces an effective method to analyze their relationship, challenging previous assumptions.

Findings

No general connection between energy diffusion and heat conduction in 1D systems.

A possible general connection exists between heat diffusion and heat conduction.

Significant differences found in relaxation behaviors of local energy and heat current fluctuations.

Abstract

Heat and energy are conceptually different, but often are assumed to be the same without justification. An effective method for investigating diffusion properties in equilibrium systems is discussed. With this method, we demonstrate that for one-dimensional systems, using the indices of particles as the space variable , which has been accepted as a convention, may lead to misleading conclusions. We then show that though in one-dimensional systems there is no general connection between energy diffusion and heat conduction, however, a general connection between heat diffusion and heat conduction may exist. Relaxation behavior of local energy current fluctuations and that of local heat current fluctuations are also studied. We find that they are significantly different, though the global energy current equals the globe heat current.