Quantum Refrigerator and the III-law of Thermodynamics

TL;DR

This paper investigates the fundamental limits of cooling quantum systems to absolute zero by analyzing the rate at which temperature decreases, revealing that the cooling process's exponent is determined by the cold bath's properties.

Contribution

It provides a dynamic quantification of the third law of thermodynamics for quantum refrigerators, showing the exponent's independence from the working medium and driver characteristics.

Findings

The cooling rate exponent is universal across different refrigerator types.

The exponent depends solely on the cold bath's properties and interactions.

The study compares heat-driven and power-driven refrigerators, finding identical exponents.

Abstract

The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to the absolute zero. The III-law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent {\zeta} of the cooling process dT(t)/dt \sim -T^{\zeta} when approaching the absolute zero, T \rightarrow 0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled 2-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cooled, a hot bath as an entropy sink, and a driving bath which is the source of cooling power. A heat driven refrigerator (absorption refrigerator) is compared to a power driven refrigerator. When optimized both cases lead to the same exponent {\zeta}, showing a lack of dependence on the form of the working medium and the characteristics of the drivers. The characteristic exponent is therefore determined by the properties of the cold reservoir and its interaction with the system. Two generic heat baths models are considered, a bath composed of harmonic oscillators and a bath composed from ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the III-law are discussed. In the appendix the theory of periodicaly driven open systems and its implication to thermodynamics is outlined.