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 (θ ≡ 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 vice versa. A reasonable compromise is achieved by optimizing the product of the heat-power and efficiency over the Hamiltonian of the two systems. The efficiency is then found to be bounded from below by [formula see text] (an analog of the Curzon-Ahlborn efficiency), besides being bound from above by the Carnot efficiency [formula see text]. The lower bound is reached in the equilibrium limit θ → 1. The Carnot bound is reached (for a finite power and a finite amount of heat transferred per cycle) for ln n >> 1. If the above maximization is constrained by assuming homogeneous energy spectra for both systems, the efficiency is bounded from above by ζ CA and converges to it for n >> 1.