Advertisement

Thermodynamics of Memories

  • Takahiro Sagawa
Chapter
Part of the Springer Theses book series (Springer Theses)

Abstract

Maxwell’s demon  [1, 2] can be formulated as a feedback controller acting on thermodynamic systems, and has a memory that stores measurement outcomes.The fundamental energy cost needed for the memory during information processing has been a topic of numerous discussions [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], which is fundamentally related to the consistency between the demon and the second law of thermodynamics. In this chapter, we discuss the thermodynamic properties of the demon’s memory based on recent advancements [5, 6, 17, 18, 19, 20, 21, 22, 23, 24, 25]. In particular, we identify the fundamental energy cost needed for the measurement and information erasure [23, 24, 25], which is the second main part of this thesis. Our result reduces to the celebrated Landauer principle [8] for special cases. We also discuss a new resolution of the paradox of Maxwell’s demon based on our results. For simplicity, we consider the case in which there is a single heat bath in this chapter.

Keywords

Density Operator Shannon Information Canonical Distribution Minimal Energy Cost Arbitrary Probability Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    J.C. Maxwell, Theory of Heat (Appleton, London, 1871)Google Scholar
  2. 2.
    L. Szilard, Z. Phys. 53, 840 (1929)ADSMATHCrossRefGoogle Scholar
  3. 3.
    H.S. Leff, A.F. Rex (eds.), Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing (Princeton University Press, New Jersey, 2003)Google Scholar
  4. 4.
    K. Maruyama, F. Nori, V. Vedral, Rev. Mod. Phys. 81, 1 (2009)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    O.J.E. Maroney, in Information Processing and Thermodynamic Entropy, ed. by Edward N. Zalta. The Stanford Encyclopedia of Philosophy, Fall 2009 edn. (Institute of Physics Publishing, Philadelphia, 2009).Google Scholar
  6. 6.
    T. Sagawa, M. Ueda, Information Thermodynamics: Maxwell’s Demon in Nonequilibrium dynamics, arXiv:1111.5769 (2011); To appear in R. Klages, W. Just, C, Jarzynski (eds.) Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond (Wiley-VCH, Weinheim, 2012).Google Scholar
  7. 7.
    L. Brillouin, J. Appl. Phys. 22, 334 (1951)MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    R. Landauer, IBM J. Res. Dev. 5, 183 (1961)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    C.H. Bennett, Int. J. Theor. Phys. 21, 905 (1982)CrossRefGoogle Scholar
  10. 10.
    W.H. Zurek, Nature 341, 119 (1989)ADSCrossRefGoogle Scholar
  11. 11.
    W.H. Zurek, Phys. Rev. A 40, 4731 (1989)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    K. Shizume, Phys. Rev. E 52, 3495 (1995)ADSCrossRefGoogle Scholar
  13. 13.
    R. Landauer, Science 272, 1914 (1996)MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    H. Matsueda, E. Goto, K-F. Loe, RIMS Kôkyûroku 1013, 187 (1997)Google Scholar
  15. 15.
    B. Piechocinska, Phys. Rev. A 61, 062314 (2000)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    C.H. Bennett, Stud. Hist. Phil. Mod. Phys. 34, 501 (2003)MATHCrossRefGoogle Scholar
  17. 17.
    A.E. Allahverdyan, T.M. Nieuwenhuizen, Phys. Rev. E 64, 0561171 (2001)CrossRefGoogle Scholar
  18. 18.
    C. Horhammer, H. Buttner, J. Stat. Phys. 133, 1161 (2008)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    M.M. Barkeshli, arXiv:cond-mat/0504323 (2005).Google Scholar
  20. 20.
    J.D. Norton, Stud. Hist. Phil. Mod. Phys. 36, 375 (2005)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    O.J.E. Maroney, Phys. Rev. E 79, 031105 (2009)MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    S. Turgut, Phys. Rev. E 79, 041102 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    T. Sagawa, M. Ueda, Phys. Rev. Lett. 102, 250602 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    T. Sagawa, M. Ueda, Phys. Rev. Lett. 106, 189901(E) (2011).Google Scholar
  25. 25.
    T. Sagawa, Prog. Theor. Phys. 127, 1 (2012)ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Japan 2012

Authors and Affiliations

  1. 1.Kyoto UniversityKyotoJapan

Personalised recommendations