Microscopic Quantum Mechanical Foundation of Fourier's Law

TL;DR

This paper reviews recent advances in nonequilibrium quantum thermodynamics, focusing on the microscopic quantum foundations of heat transport in small systems relevant to nanoscale devices.

Contribution

It provides a comprehensive overview of the theoretical developments in quantum thermodynamics related to heat transport at the nanoscale.

Findings

Quantum effects significantly influence heat transport at small scales.

Recent theoretical models improve understanding of energy relaxation in quantum systems.

Foundations of Fourier's law are being extended to quantum regimes.

Abstract

Besides the growing interest in old concepts like temperature and entropy at the nanoscale, theories of relaxation and transport have recently regained a lot of attention. With the electronic circuits and computer chips getting smaller and smaller, a fresh look should be appropriate on the equilibrium and nonequilibrium thermodynamics at small length scales far below the thermodynamic limit, i.e. on the theoretical understanding of original macroscopic processes, e.g. transport of energy, heat, charge, mass, magnetization etc. Only from the foundations of a theory its limits of applicability may be inferred. This review tries to give an overview of the background and recent developments in the field of nonequilibrium quantum thermodynamics focusing on the transport of heat in small quantum systems.