Optimal refrigerator

Armen E. Allahverdyan, Karen Hovhannisyan, and Guenter Mahler
Phys. Rev. E 81, 051129 – Published 20 May 2010

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 Th and Tc, respectively (θTc/Th<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 ζCA=11θ1 (an analog of the Curzon-Ahlborn efficiency), besides being bound from above by the Carnot efficiency ζC=11θ1. The lower bound is reached in the equilibrium limit θ1. The Carnot bound is reached (for a finite power and a finite amount of heat transferred per cycle) for lnn1. If the above maximization is constrained by assuming homogeneous energy spectra for both systems, the efficiency is bounded from above by ζCA and converges to it for n1.

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  • Received 18 December 2009

DOI:https://doi.org/10.1103/PhysRevE.81.051129

©2010 American Physical Society

Authors & Affiliations

Armen E. Allahverdyan1, Karen Hovhannisyan1, and Guenter Mahler2

  • 1Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia
  • 2Institute of Theoretical Physics I, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

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Issue

Vol. 81, Iss. 5 — May 2010

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