Advertisement

Second Law, Entropy Production, and Reversibility in Thermodynamics of Information

  • Takahiro Sagawa
Chapter

Abstract

We present a pedagogical review of the fundamental concepts in thermodynamics of information, by focusing on the second law of thermodynamics and the entropy production. Especially, we discuss the relationship among thermodynamic reversibility, logical reversibility, and heat emission in the context of the Landauer principle and clarify that these three concepts are fundamentally distinct to each other. We also discuss thermodynamics of measurement and feedback control by Maxwell’s demon. We clarify that the demon and the second law are indeed consistent in the measurement and the feedback processes individually, by including the mutual information to the entropy production.

Notes

Acknowledgements

The author is grateful to Masahito Ueda, John Bechhoefer, Jordan M. Horowitz, and Naoto Shiraishi for a lot of valuable comments, and to Christian Van den Broeck, Massimiliano Esposito, and Udo Seifert for valuable suggestions. This work is supported by JSPS KAKENHI Grant No. JP16H02211 and No. JP25103003.

References

  1. 1.
    J.C. Maxwell, Theory of Heat (Appleton, London, 1871)Google Scholar
  2. 2.
    L. Szilard, Z. Phys. 53, 840 (1929)CrossRefGoogle Scholar
  3. 3.
    C. Shannon, Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)Google Scholar
  4. 4.
    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
  5. 5.
    L. Brillouin, J. Appl. Phys. 22, 334 (1951)MathSciNetCrossRefGoogle Scholar
  6. 6.
    R. Landauer, IBM J. Res. Dev. 5, 183 (1961)CrossRefGoogle Scholar
  7. 7.
    C.H. Bennett, Int. J. Theor. Phys. 21, 905 (1982)CrossRefGoogle Scholar
  8. 8.
    W.H. Zurek, Nature 341, 119 (1989)CrossRefGoogle Scholar
  9. 9.
    R. Landauer, Science 272, 1914 (1996)MathSciNetCrossRefGoogle Scholar
  10. 10.
    H. Matsueda, E. Goto, K.-F. Loe, RIMS Kôkyûroku 1013, 187 (1997)Google Scholar
  11. 11.
    D.J. Evans, E.G.D. Cohen, G.P. Morris, Phys. Rev. Lett. 71, 2401 (1993)CrossRefGoogle Scholar
  12. 12.
    G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)CrossRefGoogle Scholar
  13. 13.
    B. Gaveau, L. Schulman, Phys. Lett. A 229, 347–353 (1997)MathSciNetCrossRefGoogle Scholar
  14. 14.
    C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)CrossRefGoogle Scholar
  15. 15.
    G.E. Crooks, Phys. Rev. E 60, 2721 (1999)CrossRefGoogle Scholar
  16. 16.
    C. Jarzynski, J. Stat. Phys. 98, 77 (2000)MathSciNetCrossRefGoogle Scholar
  17. 17.
    D.J. Evans, D.J. Searles, Adv. Phys. 51, 1529 (2002)CrossRefGoogle Scholar
  18. 18.
    U. Seifert, Phys. Rev. Lett. 95, 040602 (2005)CrossRefGoogle Scholar
  19. 19.
    R. Kawai, J.M.R. Parrondo, C. Van den Broeck, Phys. Rev. Lett. 98, 080602 (2007)CrossRefGoogle Scholar
  20. 20.
    M. Esposito, C. Van den Broeck, Europhys. Lett. 95, 40004 (2011)CrossRefGoogle Scholar
  21. 21.
    K. Sekimoto, Stochastic Energitics (Springer, Berlin/Heidelber, 2010)zbMATHCrossRefGoogle Scholar
  22. 22.
    C. Jarzynski, Ann. Rev. Condens. Matter Phys. 2, 329 (2011)CrossRefGoogle Scholar
  23. 23.
    U. Seifert, Rep. Prog. Phys. 75, 126001 (2012).CrossRefGoogle Scholar
  24. 24.
    K. Kawasaki, J.D. Gunton, Phys. Rev. A 8, 2048 (1973)CrossRefGoogle Scholar
  25. 25.
    J. Schnakenberg, Rev. Mod. Phys. 48, 571 (1976)MathSciNetCrossRefGoogle Scholar
  26. 26.
    G.N. Bochkov, Yu. E. Kuzovlev, Zh. Eksp. Teor. Fiz. 72, 238–247 (1977)Google Scholar
  27. 27.
    C. Van den Broeck, Selforganization by nonlinear irreversible processes, in Proceedings of the Third International Conference, Kühlungsborn, GDR, 18–22 March 1985, ed. by W. Ebeling, H. Ulbricht (Springer, Berlin, 1985), pp. 57–61Google Scholar
  28. 28.
    C.Y. Mou, J.-L. Luo, G. Nicolis, J. Chem. Phys. 84, 7011 (1986)CrossRefGoogle Scholar
  29. 29.
    J.M.R. Parrondo, J.M. Horowitz, T. Sagawa, Nat. Phys. 11, 131 (2015)CrossRefGoogle Scholar
  30. 30.
    K. Shizume, Phys. Rev. E 52, 3495 (1995)CrossRefGoogle Scholar
  31. 31.
    B. Piechocinska, Phys. Rev. A 61, 062314 (2000)MathSciNetCrossRefGoogle Scholar
  32. 32.
    M.M. Barkeshli, arXiv:cond-mat/0504323 (2005)Google Scholar
  33. 33.
    R. Dillenschneider, E. Lutz, Phys. Rev. Lett. 102, 210601 (2009)CrossRefGoogle Scholar
  34. 34.
    S. Turgut, Phys. Rev. E 79, 041102 (2009)CrossRefGoogle Scholar
  35. 35.
    T. Sagawa, M. Ueda, Phys. Rev. Lett. 102, 250602 (2009); 106, 189901(E) (2011)CrossRefGoogle Scholar
  36. 36.
    D. Reeb, M.M. Wolf, New J. Phys. 16, 103011 (2014)CrossRefGoogle Scholar
  37. 37.
    T. Sagawa, J. Stat. Mech. P03025 (2014)Google Scholar
  38. 38.
    H. Touchette, S. Lloyd, Phys. Rev. Lett. 84, 1156 (2000)CrossRefGoogle Scholar
  39. 39.
    H. Touchette, S. Lloyd, Phys. A 331, 140 (2004)MathSciNetCrossRefGoogle Scholar
  40. 40.
    K.H. Kim, H. Qian, Phys. Rev. E 75, 022102 (2007)CrossRefGoogle Scholar
  41. 41.
    T. Sagawa, M. Ueda, Phys. Rev. Lett. 100, 080403 (2008)CrossRefGoogle Scholar
  42. 42.
    F.J. Cao, M. Feito, Phys. Rev. E 79, 041118 (2009)CrossRefGoogle Scholar
  43. 43.
    T. Sagawa, M. Ueda, Phys. Rev. Lett. 104, 090602 (2010)CrossRefGoogle Scholar
  44. 44.
    T. Sagawa, Prog. Theor. Phys. 127, 1 (2012)CrossRefGoogle Scholar
  45. 45.
    J.M. Horowitz, S. Vaikuntanathan, Phys. Rev. E 82, 061120 (2010)CrossRefGoogle Scholar
  46. 46.
    T. Sagawa, M. Ueda, Phys. Rev. E 85, 021104 (2012)CrossRefGoogle Scholar
  47. 47.
    D. Abreu, U. Seifert, Phys. Rev. Lett. 108, 030601 (2012)CrossRefGoogle Scholar
  48. 48.
    S. Lahiri, S. Rana, A.M. Jayannavar, J. Phys. A: Math. Theor. 45, 065002 (2012)CrossRefGoogle Scholar
  49. 49.
    S. Still, D.A. Sivak, A.J. Bell, G.E. Crooks, Phys. Rev. Lett. 109, 120604 (2012)CrossRefGoogle Scholar
  50. 50.
    T. Sagawa, M. Ueda, Phys. Rev. Lett. 109, 180602 (2012)CrossRefGoogle Scholar
  51. 51.
    T. Sagawa, M. Ueda, New J. Phys. 15, 125012 (2013)MathSciNetCrossRefGoogle Scholar
  52. 52.
    S. Ciliberto, Phys. Rev. X 7, 021051 (2017)Google Scholar
  53. 53.
    S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, M. Sano, Nat. Phys. 6, 988 (2010)CrossRefGoogle Scholar
  54. 54.
    A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, E. Lutz, Nature 483, 187–189 (2012)CrossRefGoogle Scholar
  55. 55.
    E. Roldan, I.A. Martinez, J.M.R. Parrondo, D. Petrov, Nat. Phys. 10, 457 (2014)CrossRefGoogle Scholar
  56. 56.
    J.V. Koski, V.F. Maisi, T. Sagawa, J.P. Pekola, Phys. Rev. Lett. 113, 030601 (2014)CrossRefGoogle Scholar
  57. 57.
    J.V. Koski, A. Kutvonen, I.M. Khaymovich, T. Ala-Nissila, J.P. Pekola, Phys. Rev. Lett. 115, 260602 (2015)CrossRefGoogle Scholar
  58. 58.
    K. Chida, S. Desai, K. Nishiguchi, A. Fujiwara, Nat. Commun. 8, 15310 (2017)CrossRefGoogle Scholar
  59. 59.
    A. Bérut, A. Petrosyan, S. Ciliberto, Europhys. Lett. 103, 60002 (2013)CrossRefGoogle Scholar
  60. 60.
    Y. Jun, M. Gavrilov, J. Bechhoefer, Phys. Rev. Lett. 113, 190601 (2014)CrossRefGoogle Scholar
  61. 61.
    M. Gavrilov, J. Bechhoefer, Phys. Rev. Lett. 117, 200601 (2016)MathSciNetCrossRefGoogle Scholar
  62. 62.
    M. Gavrilov, R. Chétrite, J. Bechhoefer, Proc. Natl. Acad. Sci. USA 114, 11097–11102 (2017)CrossRefGoogle Scholar
  63. 63.
    J. Hong, B. Lambson, S. Dhuey, J. Bokor, Sci. Adv. 11, e1501492 (2016)CrossRefGoogle Scholar
  64. 64.
    M. Lopez-Suarez, I. Neri, L. Gammaitoni, Nat. Commun. 7, 12068 (2016)CrossRefGoogle Scholar
  65. 65.
    J.P.P. Silva et al., Proc. R. Soc. A 472, 20150813 (2016)CrossRefGoogle Scholar
  66. 66.
    M.D. Vidrighin, O. Dahlsten, M. Barbieri, M.S. Kim, V. Vedral, I.A. Walmsley, Phys. Rev. Lett. 116, 050401 (2016)CrossRefGoogle Scholar
  67. 67.
    P.A. Camati et al., Phys. Rev. Lett. 117, 240502 (2016)CrossRefGoogle Scholar
  68. 68.
    N. Cottet et al., Proc. Natl. Acad. Sci. USA 114, 7561–7564 (2017)CrossRefGoogle Scholar
  69. 69.
    Y. Masuyama, K. Funo, Y. Murashita, A. Noguchi, S. Kono, Y. Tabuchi, R. Yamazaki, M. Ueda, Y. Nakamura, arXiv:1709.00548 (2017)Google Scholar
  70. 70.
    H.B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edn. (Wiley, New York, 1985)zbMATHGoogle Scholar
  71. 71.
    E.H. Lieb, J. Yngvasonb, Phys. Rep. 314, 669 (1999)CrossRefGoogle Scholar
  72. 72.
    D. Kondepudi, I. Prigogine, From Heat Engines to Dissipative Structures (Wiley, New York, 1998)zbMATHGoogle Scholar
  73. 73.
    M. Gavrilov, J. Bechhoefer, Europhys. Lett. 114, 50002 (2016)CrossRefGoogle Scholar
  74. 74.
    N. Shiraishi, K. Saito, H. Tasaki, Phys. Rev. Lett. 117, 190601 (2016)CrossRefGoogle Scholar
  75. 75.
    F. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)CrossRefGoogle Scholar
  76. 76.
    M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)CrossRefGoogle Scholar
  77. 77.
    T.M. Cover, J.A. Thomas, Elements of Information Theory (Wiley, New York, 1991)zbMATHCrossRefGoogle Scholar
  78. 78.
    N.G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edn. (North-Holland Personal Library, 2007)Google Scholar
  79. 79.
    W.C. Gardiner, Handbook of Stochastic Methods, 3rd edn. (Springer, Berlin, 2004)zbMATHCrossRefGoogle Scholar
  80. 80.
    C. Moore, S. Mertens, The Nature of Computation (Oxford University Press, Oxford, 2011)zbMATHCrossRefGoogle Scholar
  81. 81.
    K. Jacobs, Phys. Rev. A 80, 012322 (2009)CrossRefGoogle Scholar
  82. 82.
    J.M. Horowitz, J.M.R. Parrondo, Europhys. Lett. 95, 10005 (2011)CrossRefGoogle Scholar
  83. 83.
    J.M. Horowitz, J.M.R. Parrondo, New J. Phys. 13, 123019 (2011)CrossRefGoogle Scholar
  84. 84.
    D. Abreu, U. Seifert, Europhys. Lett. 94, 10001 (2011)CrossRefGoogle Scholar
  85. 85.
    J.M. Horowitz, T. Sagawa, J.M.R. Parrondo, Phys. Rev. Lett. 111, 010602 (2013)CrossRefGoogle Scholar
  86. 86.
    C. Kwon, Phys. Rev. E 95, 042103 (2017)CrossRefGoogle Scholar
  87. 87.
    D. Andrieux, P. Gaspard, J. Stat. Mech. Theor. Exp. P02006 (2007)Google Scholar
  88. 88.
    K. Saito, Y. Utsumi, Phys. Rev. B 78, 115429 (2008)CrossRefGoogle Scholar
  89. 89.
    A.E. Allahverdyan, D. Janzing, G. Mahler, J. Stat. Mech. Theor. Exp. P09011 (2009)Google Scholar
  90. 90.
    Y. Fujitani, H. Suzuki, J. Phys. Soc. Jpn. 79, 104003 (2010)CrossRefGoogle Scholar
  91. 91.
    P. Strasberg, G. Schaller, T. Brandes, M. Esposito, Phys. Rev. Lett. 110, 040601 (2013)CrossRefGoogle Scholar
  92. 92.
    S. Ito, T. Sagawa, Phys. Rev. Lett. 111, 180603 (2013)CrossRefGoogle Scholar
  93. 93.
    D. Hartich, A.C. Barato, U. Seifert, J. Stat. Mech. P02016 (2014)Google Scholar
  94. 94.
    T. Munakata, M.L. Rosinberg, Phys. Rev. Lett. 112, 180601 (2014)CrossRefGoogle Scholar
  95. 95.
    J.M. Horowitz, M. Esposito, Phys. Rev. X 4, 031015 (2014)Google Scholar
  96. 96.
    J.M. Horowitz, H. Sandberg, New J. Phys. 16, 125007 (2014)MathSciNetCrossRefGoogle Scholar
  97. 97.
    N. Shiraishi, T. Sagawa, Phys. Rev, E 91, 012130 (2015)Google Scholar
  98. 98.
    N. Shiraishi, S. Ito, K. Kawaguchi, T. Sagawa, New J. Phys. 17, 045012 (2015)MathSciNetCrossRefGoogle Scholar
  99. 99.
    S. Yamamoto, S. Ito, N. Shiraishi, T. Sagawa, Phys. Rev. E 94, 052121 (2016)CrossRefGoogle Scholar
  100. 100.
    M.L. Rosinberg, J.M. Horowitz, Eur. Phys. Lett. 116, 10007 (2016)CrossRefGoogle Scholar
  101. 101.
    D. Hartich, A.C. Barato, U. Seifert, Phys. Rev. E 93, 022116 (2016)CrossRefGoogle Scholar
  102. 102.
    T. Schreiber, Phys. Rev. Lett. 85, 461 (2000)CrossRefGoogle Scholar
  103. 103.
    D. Mandal, C. Jarzynski, Proc. Natl. Acad. Sci. USA 109, 11641 (2012)CrossRefGoogle Scholar
  104. 104.
    S. Deffner, C. Jarzynski, Phys. Rev. X 3, 041003 (2013)Google Scholar
  105. 105.
    A.C. Barato, U. Seifert, Phys. Rev. Lett. 112, 090601 (2014)CrossRefGoogle Scholar
  106. 106.
    A.C. Barato, U. Seifert, Phys. Rev. E 90, 042150 (2014)CrossRefGoogle Scholar
  107. 107.
    N. Merhav, J. Stat. Mech. P06037 (2015)Google Scholar
  108. 108.
    A.B. Boyd, D. Mandal, J.P. Crutchfield, New J. Phys. 18, 023049 (2016)CrossRefGoogle Scholar
  109. 109.
    P. Strasberg, G. Schaller, T. Brandes, M. Esposito, Phys. Rev. X 7, 021003 (2017)Google Scholar
  110. 110.
    N. Shiraishi, T. Matsumoto, T. Sagawa, New J. Phys. 18, 013044 (2016)CrossRefGoogle Scholar
  111. 111.
    A.B. Boyd, J.P. Crutchfield, Phys. Rev. Lett. 116, 190601 (2016)CrossRefGoogle Scholar
  112. 112.
    A.B. Boyd, D. Mandal, P.M. Riechers, J.P. Crutchfield, Phys. Rev. Lett. 118, 220602 (2017)CrossRefGoogle Scholar
  113. 113.
    G. Lan, P. Satori, S. Neumann, V. Sourjik, Y. Tu, Nat. Phys. 8, 422–428 (2012)CrossRefGoogle Scholar
  114. 114.
    P. Mehta, D.J. Schwab, Proc. Natl. Acad. Sci. USA 109, 17978 (2012)CrossRefGoogle Scholar
  115. 115.
    A.C. Barato, D. Hartich, U. Seifert, Phys. Rev. E 87, 042104 (2013)CrossRefGoogle Scholar
  116. 116.
    A.C. Barato, D. Hartich, U. Seifert, New J. Phys. 16, 103024 (2014)MathSciNetCrossRefGoogle Scholar
  117. 117.
    A.H. Lang, C.K. Fisher, T. Mora, P. Mehta, Phys. Rev. Lett. 113, 148103 (2014)CrossRefGoogle Scholar
  118. 118.
    P. Sartori, L. Granger, C.F. Lee, J.M. Horowitz, PLoS Compt. Biol. 10, e1003974 (2014)CrossRefGoogle Scholar
  119. 119.
    S. Ito, T. Sagawa, Nat. Commun. 6, 7498 (2015)CrossRefGoogle Scholar
  120. 120.
    T. J. Kobayashi, Y. Sughiyama, Phys. Rev. Lett. 115, 238102 (2015)CrossRefGoogle Scholar
  121. 121.
    P. Sartori, S. Pigolotti, Phys. Rev. X 5, 041039 (2015)Google Scholar
  122. 122.
    T.E. Ouldridge, P.R. ten Wolde, Phys, Rev. Lett. 118, 158103 (2017)CrossRefGoogle Scholar
  123. 123.
    T.E. Ouldridge, C.C. Govern, P.R. ten Wolde, Phys, Rev. X 7, 021004 (2017)Google Scholar
  124. 124.
    T. Matsumoto, T. Sagawa, arXiv:1711.00264 (2017)Google Scholar
  125. 125.
    J. Kurchan, arXiv:cond-mat/0007360 (2000)Google Scholar
  126. 126.
    H. Tasaki, arXiv:cond-mat/0009244 (2000)Google Scholar
  127. 127.
    M. Esposito, U. Harbola, S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009)CrossRefGoogle Scholar
  128. 128.
    T. Campisi, P. Hanggi, P. Talkner, Rev. Mod. Phys. 83, 771 (2011)CrossRefGoogle Scholar
  129. 129.
    T. Sagawa, arXiv:1202.0983 (2012); Chapter of Lectures on Quantum Computing, Thermodynamics and Statistical Physics. Kinki University Series on Quantum Computing (World Scientific, Singapore, 2012)Google Scholar
  130. 130.
    À. M. Alhambra, L. Masanes, J. Oppenheim, C. Perry, Phys. Rev. X 6, 041017 (2016)Google Scholar
  131. 131.
    W.H. Zurek, in Frontiers of Nonequilibrium Statistical Physics, ed. by G.T. Moore, M.O. Scully. NATO ASI Series (Series B: Physics), vol. 135 (Springer, Boston, 1986). arXiv:quant-ph/0301076Google Scholar
  132. 132.
    S.W. Kim, T. Sagawa, S. De Liberato, M. Ueda, Phys. Rev. Lett. 106, 070401 (2011)CrossRefGoogle Scholar
  133. 133.
    S. Lloyd, Phys. Rev. A 39, 5378 (1989)MathSciNetCrossRefGoogle Scholar
  134. 134.
    M.A. Nielsen, C.M. Caves, B. Schumacher, H. Barnum, Proc. R. Soc. Lond. A 454, 277 (1998)CrossRefGoogle Scholar
  135. 135.
    Y. Morikuni, H. Tasaki, J. Stat. Phys. 143, 1 (2011)MathSciNetCrossRefGoogle Scholar
  136. 136.
    L. del Rio, J. Aberg, R. Renner, O. Dahlsten, V. Vedral, Nature 474, 61 (2011)CrossRefGoogle Scholar
  137. 137.
    K. Funo, Y. Watanabe, M. Ueda, Phys. Rev. E 88, 052121 (2013)CrossRefGoogle Scholar
  138. 138.
    H. Tajima, Phys. Rev. E 88, 042143 (2013)CrossRefGoogle Scholar
  139. 139.
    J.J. Park, K.-H. Kim, T. Sagawa, S.W. Kim, Phys. Rev. Lett. 111, 230402 (2013)CrossRefGoogle Scholar
  140. 140.
    J. Goold, M. Huber, A. Riera, L. del Rio, P. Skrzypzyk, J. Phys. A: Math. Theor. 49, 143001 (2016)CrossRefGoogle Scholar
  141. 141.
    M. Horodecki, J. Oppenheim, Nat. Commun. 4, 2059 (2013)CrossRefGoogle Scholar
  142. 142.
    F.G.S.L. Brandão, M. Horodecki, N.H.Y. Ng, J. Oppenheim, S. Wehner, Proc. Natl. Acad. Sci. 112, 3275 (2015)CrossRefGoogle Scholar
  143. 143.
    S. Popescu, A.J. Short, A. Winter, Nat. Phys. 2, 754–758 (2006)CrossRefGoogle Scholar
  144. 144.
    M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854–858 (2008)CrossRefGoogle Scholar
  145. 145.
    E. Iyoda, K. Kaneko, T. Sagawa, Phys. Rev. Lett. 119, 100601 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied PhysicsThe University of TokyoTokyoJapan

Personalised recommendations