Thermodynamic limits of dynamic cooling

Armen E. Allahverdyan, Karen V. Hovhannisyan, Dominik Janzing, and Guenter Mahler
Phys. Rev. E 84, 041109 – Published 10 October 2011

Abstract

We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature Tmin>0 reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir and over the reservoir energy spectrum. The minimal work needed to reach Tmin grows as 1/Tmin. This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above Tmin. Our results on Tmin>0 prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. We also study cooling via a reservoir consisting of N1 identical spins. Here we show that Tmin1N and find the maximal cooling compatible with the minimal work determined by the free energy. Finally we discuss cooling by reservoir with an initially microcanonic state and show that although a purely microcanonic state can yield the zero temperature, the unattainability is recovered when taking into account imperfections in preparing the microcanonic state.

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  • Received 20 March 2011

DOI:https://doi.org/10.1103/PhysRevE.84.041109

©2011 American Physical Society

Authors & Affiliations

Armen E. Allahverdyan1, Karen V. Hovhannisyan1, Dominik Janzing2, and Guenter Mahler3

  • 1Yerevan Physics Institute, Alikhanian Brothers Street 2, Yerevan 375036, Armenia
  • 2MPI for Intelligent Systems, Spemannstrasse 38, D-72076 Tuebingen, Germany
  • 3Institute of Theoretical Physics I, University of Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany

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Vol. 84, Iss. 4 — October 2011

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