Thermodynamic and quantum bounds on nonlinear DC thermoelectric transport

TL;DR

This paper establishes fundamental thermodynamic and quantum bounds on nonlinear DC thermoelectric transport in quantum systems, impacting the limits of heat engines, refrigerators, and cooling to absolute zero.

Contribution

It derives three fundamental bounds, including a quantum bound, on nonlinear thermoelectric transport in quantum systems modeled by nonlinear scattering theory.

Findings

Quantum bound limits the efficiency of mesoscopic heat engines.

Quantum bound implies the unattainability of absolute zero temperature in finite time.

Thermodynamic bounds constrain nonlinear heating, work, and entropy production.

Abstract

I consider the non-equilibrium DC transport of electrons through a quantum system with a thermoelectric response. This system may be any nanostructure or molecule modeled by the nonlinear scattering theory which includes Hartree-like electrostatic interactions exactly, and certain dynamic interaction effects (decoherence and relaxation) phenomenologically. This theory is believed to be a reasonable model when single-electron charging effects are negligible. I derive three fundamental bounds for such quantum systems coupled to multiple macroscopic reservoirs, one of which may be superconducting. These bounds affect nonlinear heating (such as Joule heating), work and entropy production. Two bounds correspond to the first law and second law of thermodynamics in classical physics. The third bound is quantum (wavelength dependent), and is as important as the thermodynamic ones in limiting the capabilities of mesoscopic heat-engines and refrigerators. The quantum bound also leads to Nernst's unattainability principle that the quantum system cannot cool a reservoir to absolute zero in a finite time, although it can get exponentially close.