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Conclusions

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Thermodynamics of Information Processing in Small Systems

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Modern nonequilibrium statistical mechanics provides derivations of the second law of thermodynamics based on the microscopic quantum dynamics of thermodynamic systems. By combining the derivations with quantum information theory, generalizations of the second law of thermodynamics have been derived for quantum information processing such as quantum measurement, quantum feedback control, and information erasure. Moreover, generalized nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality have been derived in the presence of feedback control. These results are applicable to small thermodynamic systems that can be precisely controlled by modern experimental technologies. These results are also closely related to the fundamental problem of Maxwell’s demon, which can be regarded as a feedback controller acting on thermodynamic systems.

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References

  1. J. Kurchan, arXiv:cond-mat/0007360 (2000).

    Google Scholar 

  2. H. Tasaki, arXiv:cond-mat/0009244 (2000).

    Google Scholar 

  3. C. Jarzynski, D.K. Wójcik, Phys. Rev. Lett. 92, 230602 (2004)

    Article  ADS  Google Scholar 

  4. T. Sagawa, Second law-like inequalities with quantum relative entropy: an introduction, in Lectures on Quantum Computing, Thermodynamics and Statistical Physics. Kinki University Series on Quantum Computing (World Scientific, Singapore, 2012); e-print: arXiv:1202.0983. (To appear).

    Google Scholar 

  5. S. Lloyd, Phys. Rev. A 39, 5378 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  6. M.A. Nielsen, C.M. Caves, B. Schumacher, H. Barnum, Proc. R. Soc. Lond. A 454, 277 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. T. Sagawa, M. Ueda, Phys. Rev. Lett. 100, 080403 (2008)

    Article  ADS  Google Scholar 

  8. A.E. Allahverdyan, T.M. Nieuwenhuizen, Phys. Rev. E 64, 0561171 (2001)

    Article  Google Scholar 

  9. C. Horhammer, H. Buttner, J. Stat. Phys. 133, 1161 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  10. O.J.E. Maroney, Phys. Rev. E 79, 031105 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  11. T. Sagawa, M. Ueda, Phys. Rev. Lett. 102, 250602 (2009)

    Article  ADS  Google Scholar 

  12. T. Sagawa, M. Ueda, Phys. Rev. Lett. 106, 189901(E) (2011).

    Google Scholar 

  13. T. Sagawa, Prog. Theor. Phys. 127, 1 (2012)

    Article  ADS  MATH  Google Scholar 

  14. T. Sagawa, M. Ueda, Phys. Rev. Lett. 104, 090602 (2010)

    Article  ADS  Google Scholar 

  15. M. Ponmurugan, Phys. Rev. E 82, 031129 (2010)

    Article  ADS  Google Scholar 

  16. Y. Fujitani, H. Suzuki, J. Phys. Soc. Jpn. 79, 104003 (2010)

    Article  ADS  Google Scholar 

  17. J.M. Horowitz, S. Vaikuntanathan, Phys. Rev. E 82, 061120 (2010)

    Article  ADS  Google Scholar 

  18. S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, M. Sano, Nat. Phys. 6, 988 (2010)

    Article  Google Scholar 

  19. Y. Morikuni, H. Tasaki, J. Stat. Phys. 143, 1 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. S. Lahiri, S. Rana, A.M. Jayannavar, J. Phys. A Math. Theor. 45, 065002 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  21. D. Abreu, U. Seifert, Phys. Rev. Lett. 108, 030601 (2012)

    Article  ADS  Google Scholar 

  22. T. Sagawa, M. Ueda, Phys. Rev. E 85, 021104 (2012)

    Article  ADS  Google Scholar 

  23. J.C. Maxwell, Theory of Heat (Appleton, London, 1871)

    Google Scholar 

  24. H.S. Leff, A.F. Rex (eds.), Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing (Princeton University Press, Princeton, 2003)

    Google Scholar 

  25. K. Maruyama, F. Nori, V. Vedral, Rev. Mod. Phys. 81, 1 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. O.J.E. Maroney, Information processing and thermodynamic entropy, in The Stanford Encyclopedia of Philosophy, Fall 2009 edn., ed. by E.N. Zalta (Springer, Berlin, 2009).

    Google Scholar 

  27. T. Sagawa, M. Ueda, Information thermodynamics: Maxwell’s Demon in nonequilibrium dynamics, in Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond, ed. by R. Klages, W. Just, C. Jarzynski (Wiley-VCH, Weinheim, 2012). arXiv:1111.5769 (2011) (To appear).

    Google Scholar 

  28. J. von Neumann, Z. Phys. 57, 30 (1929) (Eng. Trans. in arXiv:1003.2133).

    Google Scholar 

  29. J.M. Deutsch, Phys. Rev. A 43, 2046 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  30. M. Srednicki, Phys. Rev. E 50, 888 (1994)

    Article  ADS  Google Scholar 

  31. H. Tasaki, Phys. Rev. Lett. 80, 1373 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. A. Sugita, RIMS Kôkyûroku, 1507, 147 (2006) (in Japanese).

    Google Scholar 

  33. S. Goldstein, J.L. Lebowitz1, R. Tumulka, N. Zanghi. Phys. Rev. Lett. 96, 050403 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  34. S. Popescu, A.J. Short, A. Winter, Nat. Phys. 2, 754 (2006)

    Article  Google Scholar 

  35. P. Reimann, Phys. Rev. Lett. 99, 160404 (2007)

    Article  ADS  Google Scholar 

  36. M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854 (2008)

    Article  ADS  Google Scholar 

  37. A. Lenard, J. Stat. Phys. 19, 575 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  38. W. Pusz, S.L. Woronowic, Commun. Math. Phys. 58, 273 (1978)

    Article  ADS  Google Scholar 

  39. H. Tasaki, arXiv:cond-mat/0009206 (2000).

    Google Scholar 

  40. M. Campisi, Stud. Hist. Phil. Mod. Phys. 39, 181 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Kyoto University, Kitashirakawa Oiwake-Cho, Sakyo-Ku, Kyoto, 606-8502, Japan

    Takahiro Sagawa

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  1. Takahiro Sagawa
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Correspondence to Takahiro Sagawa .

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Sagawa, T. (2012). Conclusions. In: Thermodynamics of Information Processing in Small Systems. Springer Theses. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54168-4_10

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