Fourier's law based on microscopic dynamics

TL;DR

This paper reviews recent advances in deriving Fourier's law from microscopic dynamics, emphasizing the role of Newtonian equations and simplified models in understanding heat conduction.

Contribution

It provides a comprehensive overview of progress in microscopic derivations of Fourier's law using computational and theoretical approaches.

Findings

Microscopic models help clarify the basis of Fourier's law.

High-precision simulations of Newton's equations support empirical observations.

Simplified systems reveal fundamental mechanisms of heat conduction.

Abstract

While Fourier's law is empirically confirmed for many substances and over an extremely wide range of thermodynamic parameters, a convincing microscopic derivation still poses difficulties. With current machines the solution of Newton's equations of motion can be obtained with high precision and for a reasonably large number of particles. For simplified model systems one thereby arrives at a deeper understanding of the microscopic basis for Fourier's law. We report on recent, and not so recent, advances.