Journal of Statistical Physics

, Volume 143, Issue 1, pp 1–10 | Cite as

Quantum Jarzynski-Sagawa-Ueda Relations



We consider a (small) quantum mechanical system which is operated by an external agent, who changes the Hamiltonian of the system according to a fixed scenario. In particular we assume that the agent (who may be called a demon) performs measurement followed by feedback, i.e., it makes a measurement of the system and changes the protocol according to the outcome. We extend to this setting the generalized Jarzynski relations, recently derived by Sagawa and Ueda for classical systems with feedback. One of the two relations by Sagawa and Ueda is derived here in error-free quantum processes, while the other is derived only when the measurement process involves classical errors. The first relation leads to a second law which takes into account the efficiency of the feedback.


Jarzynski relation Feedback Measurement Quantum system 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Evans, D.J., Cohen, E.G.D., Morriss, G.P.: Probability of second law violations in shearing steady states. Phys. Rev. Lett. 71, 2401–2404 (1993) CrossRefMATHADSGoogle Scholar
  2. 2.
    Gallavotti, G., Cohen, E.G.D.: Dynamical ensembles in nonequilibrium statistical mechanics. Phys. Rev. Lett. 74, 2694–2697 (1995). arXiv:chao-dyn/9410007 CrossRefADSGoogle Scholar
  3. 3.
    Crooks, G.E.: Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. Phys. Rev. E 60, 2721–2726 (1999). arXiv:cond-mat/9901352 CrossRefADSGoogle Scholar
  4. 4.
    Jarzynski, C.: Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690 (1997). arXiv:cond-mat/9610209 CrossRefADSGoogle Scholar
  5. 5.
    Sagawa, T., Ueda, M.: Second law of thermodynamics with discrete quantum feedback control. Phys. Rev. Lett. 100, 80403 (2008). arXiv:0710.0956 CrossRefADSGoogle Scholar
  6. 6.
    Sagawa, T., Ueda, M.: Generalized Jarzynski equality under nonequilibrium feedback control. Phys. Rev. Lett. 104, 90602 (2010). arXiv:0907.4914 CrossRefADSGoogle Scholar
  7. 7.
    Toyabe, S., Sagawa, T., Ueda, M., Muneyuki, E., Sano, M.: Experimental demonstration of information-to-energy conservation and validation of the generalized Jarzynski equality. Nat. Phys. 6, 988–992 (2010). arXiv:1009.5287 CrossRefGoogle Scholar
  8. 8.
    Campisi, M., Talkner, P., Hänggi, P.: Fluctuation theorems for continuously monitored quantum fluxes. Phys. Rev. Lett. 105, 140601 (2010). arXiv:1006.1542 CrossRefADSGoogle Scholar
  9. 9.
    Horowitz, J.M., Vaikuntanathan, S.: Nonequilibrium detailed fluctuation theorem for repeated discrete feedback. Preprint (2010). arXiv:1011.4273
  10. 10.
    Tasaki, H.: Jarzynski relations for quantum systems and some applications (2000, unpublished note). arXiv:cond-mat/0009244
  11. 11.
    Kurchan, J.: A quantum fluctuation theorem. Preprint (2000). arXiv:cond-mat/0007360
  12. 12.
    Sagawa, T.: Private communication Google Scholar
  13. 13.
    Terashima, H., Ueda, M.: Hermitian conjugate measurement. Phys. Rev. A 81, 1094–1622 (2010). arXiv:0709.1210 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of PhysicsGakushuin UniversityTokyoJapan

Personalised recommendations