# Heat flux in one-dimensional systems

## TL;DR

This paper investigates heat transport in one-dimensional classical oscillator chains, highlighting the roles of convective and conductive flux components and their dependence on temperature and pressure, revealing complex nonlocal effects.

## Contribution

It introduces a combined Lagrangian and Eulerian framework to analyze heat flux, emphasizing the significance of convective contributions in one-dimensional systems.

## Key findings

- Convective flux dominates at high temperatures, behaving gas-like.
- Convective component can be negative under negative pressure.
- Long-range correlations influence heat transport properties.

## Abstract

Understanding heat transport in one-dimensional systems remains a major challenge in theoretical physics, both from the quantum as well as from the classical point of view. In fact, steady states of one-dimensional systems are commonly characterized by macroscopic inhomogeneities, and by long range correlations, as well as large fluctuations that are typically absent in standard three-dimensional thermodynamic systems. These effects violate locality --material properties in the bulk may be strongly affected by the boundaries, leading to anomalous energy transport-- and they make more problematic the interpretation of mechanical microscopic quantities in terms of thermodynamic observables. Here, we revisit the problem of heat conduction in chains of classical nonlinear oscillators, following a Lagrangian and an Eulerian approach. The Eulerian definition of the flux is composed of a convective and a conductive component. The former component tends to prevail at large temperatures where the system behavior is increasingly gas-like. Finally, we find that the convective component tends to be negative in the presence of a negative pressure.