The quantum refrigerator: The quest for absolute zero

The emergence of the laws of thermodynamics from the laws of quantum mechanics is an unresolved issue. The generation of the third law of thermodynamics from quantum dynamics is analysed. The scaling of the optimal cooling power of a reciprocating quantum refrigerator is sought as a function of the cold bath temperature as Tc → 0. The working medium consists of noninteracting particles in a harmonic potential. Two closed-form solutions of the refrigeration cycle are analyzed, and compared to a numerical optimization scheme, focusing on cooling toward zero temperature. The optimal cycle is characterized by linear relations between the heat extracted from the cold bath, the energy level spacing of the working medium and the temperature. The scaling of the optimal cooling rate is found to be proportional to T 3/2 c giving a dynamical interpretation to the third law of thermodynamics. Copyright c © EPLA, 2009 Walter Nernst stated the third law of thermodynamics as follows: “it is impossible by any procedure, no matter how idealized, to reduce any system to the absolute zero of temperature in a finite number of operations” [1,2]. This statement has been termed the unattainability principle [3–6]. In the present study the unattainability statement is viewed dynamically as the vanishing of the cooling rate Q̇c when pumping heat from a cold bath whose temperature approaches absolute zero. Finding a limiting scaling law between the rate of cooling and temperature Q̇c ∝ T δ c quantifies the unattainability principle. The second law of thermodynamics already imposes a restriction on δ [7]. For a cyclic process entropy is generated only in the baths: σ=−Q̇c/Tc + Q̇h/Th > 0. If Q̇h stays bounded, |Q̇h| Q̇h/Th > Q̇c/Tc, and so (