Quantum refrigerators and the third law of thermodynamics
Abstract
The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to absolute zero. The third law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process (dT(t))/(dt)̃T^{ζ} when approaching absolute zero, T→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 twolevel 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 heatdriven refrigerator (absorption refrigerator) is compared to a powerdriven refrigerator. When optimized, both cases lead to the same exponent ζ, 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 bath models are considered: a bath composed of harmonic oscillators and a bath composed of ideal Bose/Fermi gas. The restrictions on the interaction Hamiltonian imposed by the third law are discussed. In the Appendices, the theory of periodically driven open systems and its implication for thermodynamics are outlined.
 Publication:

Physical Review E
 Pub Date:
 June 2012
 DOI:
 10.1103/PhysRevE.85.061126
 arXiv:
 arXiv:1205.1347
 Bibcode:
 2012PhRvE..85f1126L
 Keywords:

 05.30.d;
 03.65.Yz;
 05.70.Ln;
 07.20.Pe;
 Quantum statistical mechanics;
 Decoherence;
 open systems;
 quantum statistical methods;
 Nonequilibrium and irreversible thermodynamics;
 Heat engines;
 heat pumps;
 heat pipes;
 Quantum Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Phys.Rev. E. 85,061126 (2012)