Optimal refrigerator

Abstract

We study a refrigerator model which consists of two $n$-level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures $T_h$ and $T_c$, respectively ($\theta \equiv T_c/T_h<1$). The refrigerator functions in two steps: thermally isolated interaction between the systems driven by the external field and isothermal relaxation back to equilibrium. There is a complementarity between the power of heat transfer from the cold bath and the efficiency: the latter nullifies when the former is maximized and {\it vice versa}. A reasonable compromise is achieved by optimizing the product of the heat-power and efficiency over the Hamiltonian of the two system. The efficiency is then found to be bounded from below by ${\zeta }_{\mathrm{CA}}=\frac{1}{\sqrt{1-\theta }}-1$ (an analogue of the Curzon-Ahlborn efficiency), besides being bound from above by the Carnot efficiency ${\zeta }_{\mathrm{C}}=\frac{1}{1-\theta }-1$. The lower bound is reached in the equilibrium limit $\theta \to 1$. The Carnot bound is reached (for a finite power and a finite amount of heat transferred per cycle) for $\ln n\gg 1$. If the above maximization is constrained by assuming homogeneous energy spectra for both systems, the efficiency is bounded from above by ${\zeta }_{\mathrm{CA}}$ and converges to it for $n\gg 1$.

12 pages, 3 figures

References in corpus (8)

• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Efficiency at maximum power of Feynman's ratchet as a heat engine
• Work extremum principle: Structure and function of quantum heat engines
• The Quantum Refrigerator: The quest for absolute zero
• Stochastic pumping of heat: Approaching the Carnot efficiency
• Molecular kinetic analysis of a finite-time Carnot cycle
• Two simple models of classical heat pumps
• Small quantum networks operating as quantum thermodynamic machines

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