Cooling by Heating: Restoration of the Third Law of Thermodynamics

TL;DR

This paper modifies a quantum refrigerator model to incorporate finite energy level spacing, restoring the third law of thermodynamics and ensuring cooling to absolute zero remains unattainable in finite time.

Contribution

It introduces a simple modification to an existing quantum refrigerator model that restores the third law without altering its thermodynamic properties.

Findings

Finite energy level spacing restores the third law

The modified model prevents finite-time cooling to absolute zero

Thermodynamic properties of the original model are preserved

Abstract

We have made a simple and natural modification of a recent quantum refrigerator model presented by Cleuren et al. in Phys. Rev, Lett.108, 120603 (2012). The original model consist of two metal leads acting as heat baths, and a set of quantum dots that allow for electron transport between the baths. It was shown to violate the dynamic third law of thermodynamics (the unattainability principle, which states that cooling to absolute zero in finite time is impossible), but by taking into consideration the finite energy level spacing in metals we restore the third law, while keeping all of the original model's thermodynamic properties intact.