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Quantum thermodynamic processes: a control theory for machine cycles

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Abstract

The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this 2-dimensional control plane. Putting aside coherence we show that for a large class of quantum objects with discrete spectra and for the cycles considered the Carnot efficiency applies as a universal upper bound. In the dynamic (finite time) regime renormalized thermodynamic variables allow to include non-equilibrium phenomena in a systematic way. The machine function ceases to exist in the large speed limit; the way, in which this limit is reached, depends on the type of cycle considered.

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References

  1. A. Bejan, Advanced Engineering Thermodynamics (Wiley, N.Y., 1988)

    Google Scholar 

  2. C. Truesdell, S. Bharatha, Classical Thermodynamics as a Theory of Heat Engines (Springer, New York, Berlin, 1977)

    MATH  Google Scholar 

  3. M. Toda, R. Kubo, N. Saito, Statistical Physics 1 (Springer Berlin, New York, 1983)

    Google Scholar 

  4. J. Gemmer, M. Michel, G. Mahler, Quantum Thermodynamics (Springer, 2004)

  5. R.V. Chamberlain, Science 298, 1172 (2002)

    Article  Google Scholar 

  6. T.L. Hill, Nano Letters 1, 111 (2001)

    Article  Google Scholar 

  7. R. Alicki, J. Phys. A 12, L 103 (1979)

    Article  ADS  Google Scholar 

  8. T. Feldmann, R. Kosloff, Phys. Rev. E 68 016101 (2003)

    Google Scholar 

  9. E. Geva, R. Kosloff, J. Chem. Phys. 97, 4398 (1992)

    Article  ADS  Google Scholar 

  10. T. Jahnke, J. Birjukov, G. Mahler, Eur. Phys. J. ST (conference proceedings) 151, 167 (2007)

    Google Scholar 

  11. M.J. Henrich, G. Mahler, M. Michel, Phys. Rev. E 75, 051118 (2007)

    Google Scholar 

  12. M. Henrich, M. Michel, G. Mahler, Europhys. Lett. 76, 1058 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  13. J.P. Palao, R. Kosloff, J. Gordon, Phys. Rev. E 64, 056130 (2001)

    Google Scholar 

  14. H.T. Quan, P. Zhang, C.P. Sun, Phys. Rev. E 73, 036122 (2006)

    Google Scholar 

  15. H.E.D. Scovil, E.O. Schulz-Du Bois, Phys. Rev. Lett. 2, 262 (1959)

    Article  ADS  Google Scholar 

  16. D. Segal, A. Nitzan, Phys. Rev. E 73, 026109 (2006)

    Google Scholar 

  17. F. Tonner, G. Mahler, Phys. Rev. E 72, 066118 (2005)

    Google Scholar 

  18. L. Hackermüller, K. Hornberger, Nature 427, 711 (2004)

    Article  ADS  Google Scholar 

  19. F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)

    Article  ADS  Google Scholar 

  20. D.P. Sheehan, AIP Conf. Proc. (AIP Press, Melville, N.Y.) 643 (2002)

    Google Scholar 

  21. R. Jones, www.softmachines.org/wordpress/?p=127

  22. T.P. Cheng, Relativity, Gravitation and Cosmology (Oxford U. P., 2005)

  23. F. Rempp, M. Michel, G. Mahler, Phys. Rev. A 76, 032325 (2007)

    Google Scholar 

  24. T.D. Kieu, Phys. Rev. Lett. 93, 140403 (2004)

    Google Scholar 

  25. C.M. Bender, D.C. Brody, B.K. Meister, Proc. Royal Soc. (London) A 458, 1519 (2002)

    ADS  MathSciNet  Google Scholar 

  26. C.V.d. Broeck, Phys. Rev. Lett. 95, 190602 (2005)

  27. Y. Izumida, K. Okuda, ar**v:0802.3759 (2008)

  28. C. Tsallis, J. Stat. Phys. 52, 169 (1988)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Chair for Theoretical Physics and Applied Mathematics, Urals State Technical University, Mira 19, 620002, Jekaterinburg, Russia

    J. Birjukov

  2. Institut für Theoretische Physik 1, Universität Stuttgart, Pfaffenwaldring 57, 70550, Stuttgart, Germany

    T. Jahnke & G. Mahler

Authors
  1. J. Birjukov
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  2. T. Jahnke
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  3. G. Mahler
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Correspondence to J. Birjukov.

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Birjukov, J., Jahnke, T. & Mahler, G. Quantum thermodynamic processes: a control theory for machine cycles. Eur. Phys. J. B 64, 105–118 (2008). https://doi.org/10.1140/epjb/e2008-00270-2

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  • DOI: https://doi.org/10.1140/epjb/e2008-00270-2

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