Thermodynamics and the Quantum Transport of Particles and Entropy

TL;DR

This paper presents a unified framework linking thermodynamics and quantum transport, analyzing energy and entropy flows using models that incorporate thermoelectric effects and quantum statistics, applicable to quantum wires and conductors.

Contribution

It introduces the concept of elementary Fermi- and Bose-systems as fundamental units for quantum gases, connecting thermodynamics with quantum transport of particles and entropy.

Findings

Transport coefficients relate to thermodynamic susceptibilities.

Entropy flow exhibits quantum interference similar to electric current.

Quantum transport of entropy can be derived using elementary quantum systems.

Abstract

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balanceable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but 'elementary Fermi- or Bose-systems' as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles, but also of entropy can be derived in a concise way, and is illustrated for both ballistic quantum wires and diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.