How can we derive Fourier's Law from quantum mechanics? Exact master equation analysis

TL;DR

This paper derives Fourier's Law of heat conduction from quantum mechanics using an exact quantum master equation, demonstrating how macroscopic heat flow emerges from microscopic quantum interactions.

Contribution

It provides a rigorous derivation of Fourier's Law from quantum principles under specific assumptions, connecting microscopic exchange interactions to macroscopic energy diffusion.

Findings

Fourier's Law derived from quantum master equation

Long time limit naturally satisfies initial assumptions

Exchange interactions lead to energy diffusion in spin chains

Abstract

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first two assumptions are natural results of the long time limit. The third assumption can be satisfied by a family of interactions consisting an exchange effect. The pure exchange model directly leads to energy diffusion in a weakly coupled spin-1/2 chain.