Quantum refrigerator in the quest for the absolute zero temperature

One of the formulations of the third laws of thermodynamics is that a processes become more isentropic as one approaches the absolute zero temperatures. We examine this prediction by studying an operating model of a quantum refrigerator pumping heat from a cold to a hot reservoir. The working medium consists of a gas of noninteracting harmonic oscillators. The model can be solved in closed form in the quasi-static limit or numerically for general conditions. It is found that the isentropic limit for T_c → 0 is approached only on the expansion segment of the refrigeration cycle. The scaling of the cooling rate with temperature is shown to be consistent with the second law of thermodynamics. This scaling is also consistent with the unattainability principle which is an alternative formulation of the third law of thermodynamics.