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Energy Limits in Computation pp 101–139Cite as

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

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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.

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References

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

    Google Scholar 

  2. L. Szilard, Z. Phys. 53, 840 (1929)

    Article  Google Scholar 

  3. C. Shannon, Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)

    Google Scholar 

  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. L. Brillouin, J. Appl. Phys. 22, 334 (1951)

    Article  MathSciNet  Google Scholar 

  6. R. Landauer, IBM J. Res. Dev. 5, 183 (1961)

    Article  Google Scholar 

  7. C.H. Bennett, Int. J. Theor. Phys. 21, 905 (1982)

    Article  Google Scholar 

  8. W.H. Zurek, Nature 341, 119 (1989)

    Article  Google Scholar 

  9. R. Landauer, Science 272, 1914 (1996)

    Article  MathSciNet  Google Scholar 

  10. H. Matsueda, E. Goto, K.-F. Loe, RIMS Kôkyûroku 1013, 187 (1997)

    Google Scholar 

  11. D.J. Evans, E.G.D. Cohen, G.P. Morris, Phys. Rev. Lett. 71, 2401 (1993)

    Article  Google Scholar 

  12. G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)

    Article  Google Scholar 

  13. B. Gaveau, L. Schulman, Phys. Lett. A 229, 347–353 (1997)

    Article  MathSciNet  Google Scholar 

  14. C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)

    Article  Google Scholar 

  15. G.E. Crooks, Phys. Rev. E 60, 2721 (1999)

    Article  Google Scholar 

  16. C. Jarzynski, J. Stat. Phys. 98, 77 (2000)

    Article  MathSciNet  Google Scholar 

  17. D.J. Evans, D.J. Searles, Adv. Phys. 51, 1529 (2002)

    Article  Google Scholar 

  18. U. Seifert, Phys. Rev. Lett. 95, 040602 (2005)

    Article  Google Scholar 

  19. R. Kawai, J.M.R. Parrondo, C. Van den Broeck, Phys. Rev. Lett. 98, 080602 (2007)

    Article  Google Scholar 

  20. M. Esposito, C. Van den Broeck, Europhys. Lett. 95, 40004 (2011)

    Article  Google Scholar 

  21. K. Sekimoto, Stochastic Energitics (Springer, Berlin/Heidelber, 2010)

    Book  MATH  Google Scholar 

  22. C. Jarzynski, Ann. Rev. Condens. Matter Phys. 2, 329 (2011)

    Article  Google Scholar 

  23. U. Seifert, Rep. Prog. Phys. 75, 126001 (2012).

    Article  Google Scholar 

  24. K. Kawasaki, J.D. Gunton, Phys. Rev. A 8, 2048 (1973)

    Article  Google Scholar 

  25. J. Schnakenberg, Rev. Mod. Phys. 48, 571 (1976)

    Article  MathSciNet  Google Scholar 

  26. G.N. Bochkov, Yu. E. Kuzovlev, Zh. Eksp. Teor. Fiz. 72, 238–247 (1977)

    Google Scholar 

  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. 57–61

    Google Scholar 

  28. C.Y. Mou, J.-L. Luo, G. Nicolis, J. Chem. Phys. 84, 7011 (1986)

    Article  Google Scholar 

  29. J.M.R. Parrondo, J.M. Horowitz, T. Sagawa, Nat. Phys. 11, 131 (2015)

    Article  Google Scholar 

  30. K. Shizume, Phys. Rev. E 52, 3495 (1995)

    Article  Google Scholar 

  31. B. Piechocinska, Phys. Rev. A 61, 062314 (2000)

    Article  MathSciNet  Google Scholar 

  32. M.M. Barkeshli, arXiv:cond-mat/0504323 (2005)

    Google Scholar 

  33. R. Dillenschneider, E. Lutz, Phys. Rev. Lett. 102, 210601 (2009)

    Article  Google Scholar 

  34. S. Turgut, Phys. Rev. E 79, 041102 (2009)

    Article  Google Scholar 

  35. T. Sagawa, M. Ueda, Phys. Rev. Lett. 102, 250602 (2009); 106, 189901(E) (2011)

    Article  Google Scholar 

  36. D. Reeb, M.M. Wolf, New J. Phys. 16, 103011 (2014)

    Article  Google Scholar 

  37. T. Sagawa, J. Stat. Mech. P03025 (2014)

    Google Scholar 

  38. H. Touchette, S. Lloyd, Phys. Rev. Lett. 84, 1156 (2000)

    Article  Google Scholar 

  39. H. Touchette, S. Lloyd, Phys. A 331, 140 (2004)

    Article  MathSciNet  Google Scholar 

  40. K.H. Kim, H. Qian, Phys. Rev. E 75, 022102 (2007)

    Article  Google Scholar 

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

    Article  Google Scholar 

  42. F.J. Cao, M. Feito, Phys. Rev. E 79, 041118 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  49. S. Still, D.A. Sivak, A.J. Bell, G.E. Crooks, Phys. Rev. Lett. 109, 120604 (2012)

    Article  Google Scholar 

  50. T. Sagawa, M. Ueda, Phys. Rev. Lett. 109, 180602 (2012)

    Article  Google Scholar 

  51. T. Sagawa, M. Ueda, New J. Phys. 15, 125012 (2013)

    Article  MathSciNet  Google Scholar 

  52. S. Ciliberto, Phys. Rev. X 7, 021051 (2017)

    Google Scholar 

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

    Article  Google Scholar 

  54. A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, E. Lutz, Nature 483, 187–189 (2012)

    Article  Google Scholar 

  55. E. Roldan, I.A. Martinez, J.M.R. Parrondo, D. Petrov, Nat. Phys. 10, 457 (2014)

    Article  Google Scholar 

  56. J.V. Koski, V.F. Maisi, T. Sagawa, J.P. Pekola, Phys. Rev. Lett. 113, 030601 (2014)

    Article  Google Scholar 

  57. J.V. Koski, A. Kutvonen, I.M. Khaymovich, T. Ala-Nissila, J.P. Pekola, Phys. Rev. Lett. 115, 260602 (2015)

    Article  Google Scholar 

  58. K. Chida, S. Desai, K. Nishiguchi, A. Fujiwara, Nat. Commun. 8, 15310 (2017)

    Article  Google Scholar 

  59. A. Bérut, A. Petrosyan, S. Ciliberto, Europhys. Lett. 103, 60002 (2013)

    Article  Google Scholar 

  60. Y. Jun, M. Gavrilov, J. Bechhoefer, Phys. Rev. Lett. 113, 190601 (2014)

    Article  Google Scholar 

  61. M. Gavrilov, J. Bechhoefer, Phys. Rev. Lett. 117, 200601 (2016)

    Article  MathSciNet  Google Scholar 

  62. M. Gavrilov, R. Chétrite, J. Bechhoefer, Proc. Natl. Acad. Sci. USA 114, 11097–11102 (2017)

    Article  Google Scholar 

  63. J. Hong, B. Lambson, S. Dhuey, J. Bokor, Sci. Adv. 11, e1501492 (2016)

    Article  Google Scholar 

  64. M. Lopez-Suarez, I. Neri, L. Gammaitoni, Nat. Commun. 7, 12068 (2016)

    Article  Google Scholar 

  65. J.P.P. Silva et al., Proc. R. Soc. A 472, 20150813 (2016)

    Article  Google Scholar 

  66. M.D. Vidrighin, O. Dahlsten, M. Barbieri, M.S. Kim, V. Vedral, I.A. Walmsley, Phys. Rev. Lett. 116, 050401 (2016)

    Article  Google Scholar 

  67. P.A. Camati et al., Phys. Rev. Lett. 117, 240502 (2016)

    Article  Google Scholar 

  68. N. Cottet et al., Proc. Natl. Acad. Sci. USA 114, 7561–7564 (2017)

    Article  Google Scholar 

  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. H.B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edn. (Wiley, New York, 1985)

    MATH  Google Scholar 

  71. E.H. Lieb, J. Yngvasonb, Phys. Rep. 314, 669 (1999)

    Article  Google Scholar 

  72. D. Kondepudi, I. Prigogine, From Heat Engines to Dissipative Structures (Wiley, New York, 1998)

    MATH  Google Scholar 

  73. M. Gavrilov, J. Bechhoefer, Europhys. Lett. 114, 50002 (2016)

    Article  Google Scholar 

  74. N. Shiraishi, K. Saito, H. Tasaki, Phys. Rev. Lett. 117, 190601 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  76. M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)

    Article  Google Scholar 

  77. T.M. Cover, J.A. Thomas, Elements of Information Theory (Wiley, New York, 1991)

    Book  MATH  Google Scholar 

  78. N.G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edn. (North-Holland Personal Library, 2007)

    Google Scholar 

  79. W.C. Gardiner, Handbook of Stochastic Methods, 3rd edn. (Springer, Berlin, 2004)

    Book  MATH  Google Scholar 

  80. C. Moore, S. Mertens, The Nature of Computation (Oxford University Press, Oxford, 2011)

    Book  MATH  Google Scholar 

  81. K. Jacobs, Phys. Rev. A 80, 012322 (2009)

    Article  Google Scholar 

  82. J.M. Horowitz, J.M.R. Parrondo, Europhys. Lett. 95, 10005 (2011)

    Article  Google Scholar 

  83. J.M. Horowitz, J.M.R. Parrondo, New J. Phys. 13, 123019 (2011)

    Article  Google Scholar 

  84. D. Abreu, U. Seifert, Europhys. Lett. 94, 10001 (2011)

    Article  Google Scholar 

  85. J.M. Horowitz, T. Sagawa, J.M.R. Parrondo, Phys. Rev. Lett. 111, 010602 (2013)

    Article  Google Scholar 

  86. C. Kwon, Phys. Rev. E 95, 042103 (2017)

    Article  Google Scholar 

  87. D. Andrieux, P. Gaspard, J. Stat. Mech. Theor. Exp. P02006 (2007)

    Google Scholar 

  88. K. Saito, Y. Utsumi, Phys. Rev. B 78, 115429 (2008)

    Article  Google Scholar 

  89. A.E. Allahverdyan, D. Janzing, G. Mahler, J. Stat. Mech. Theor. Exp. P09011 (2009)

    Google Scholar 

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

    Article  Google Scholar 

  91. P. Strasberg, G. Schaller, T. Brandes, M. Esposito, Phys. Rev. Lett. 110, 040601 (2013)

    Article  Google Scholar 

  92. S. Ito, T. Sagawa, Phys. Rev. Lett. 111, 180603 (2013)

    Article  Google Scholar 

  93. D. Hartich, A.C. Barato, U. Seifert, J. Stat. Mech. P02016 (2014)

    Google Scholar 

  94. T. Munakata, M.L. Rosinberg, Phys. Rev. Lett. 112, 180601 (2014)

    Article  Google Scholar 

  95. J.M. Horowitz, M. Esposito, Phys. Rev. X 4, 031015 (2014)

    Google Scholar 

  96. J.M. Horowitz, H. Sandberg, New J. Phys. 16, 125007 (2014)

    Article  MathSciNet  Google Scholar 

  97. N. Shiraishi, T. Sagawa, Phys. Rev, E 91, 012130 (2015)

    Google Scholar 

  98. N. Shiraishi, S. Ito, K. Kawaguchi, T. Sagawa, New J. Phys. 17, 045012 (2015)

    Article  MathSciNet  Google Scholar 

  99. S. Yamamoto, S. Ito, N. Shiraishi, T. Sagawa, Phys. Rev. E 94, 052121 (2016)

    Article  Google Scholar 

  100. M.L. Rosinberg, J.M. Horowitz, Eur. Phys. Lett. 116, 10007 (2016)

    Article  Google Scholar 

  101. D. Hartich, A.C. Barato, U. Seifert, Phys. Rev. E 93, 022116 (2016)

    Article  Google Scholar 

  102. T. Schreiber, Phys. Rev. Lett. 85, 461 (2000)

    Article  Google Scholar 

  103. D. Mandal, C. Jarzynski, Proc. Natl. Acad. Sci. USA 109, 11641 (2012)

    Article  Google Scholar 

  104. S. Deffner, C. Jarzynski, Phys. Rev. X 3, 041003 (2013)

    Google Scholar 

  105. A.C. Barato, U. Seifert, Phys. Rev. Lett. 112, 090601 (2014)

    Article  Google Scholar 

  106. A.C. Barato, U. Seifert, Phys. Rev. E 90, 042150 (2014)

    Article  Google Scholar 

  107. N. Merhav, J. Stat. Mech. P06037 (2015)

    Google Scholar 

  108. A.B. Boyd, D. Mandal, J.P. Crutchfield, New J. Phys. 18, 023049 (2016)

    Article  Google Scholar 

  109. P. Strasberg, G. Schaller, T. Brandes, M. Esposito, Phys. Rev. X 7, 021003 (2017)

    Google Scholar 

  110. N. Shiraishi, T. Matsumoto, T. Sagawa, New J. Phys. 18, 013044 (2016)

    Article  Google Scholar 

  111. A.B. Boyd, J.P. Crutchfield, Phys. Rev. Lett. 116, 190601 (2016)

    Article  Google Scholar 

  112. A.B. Boyd, D. Mandal, P.M. Riechers, J.P. Crutchfield, Phys. Rev. Lett. 118, 220602 (2017)

    Article  Google Scholar 

  113. G. Lan, P. Satori, S. Neumann, V. Sourjik, Y. Tu, Nat. Phys. 8, 422–428 (2012)

    Article  Google Scholar 

  114. P. Mehta, D.J. Schwab, Proc. Natl. Acad. Sci. USA 109, 17978 (2012)

    Article  Google Scholar 

  115. A.C. Barato, D. Hartich, U. Seifert, Phys. Rev. E 87, 042104 (2013)

    Article  Google Scholar 

  116. A.C. Barato, D. Hartich, U. Seifert, New J. Phys. 16, 103024 (2014)

    Article  MathSciNet  Google Scholar 

  117. A.H. Lang, C.K. Fisher, T. Mora, P. Mehta, Phys. Rev. Lett. 113, 148103 (2014)

    Article  Google Scholar 

  118. P. Sartori, L. Granger, C.F. Lee, J.M. Horowitz, PLoS Compt. Biol. 10, e1003974 (2014)

    Article  Google Scholar 

  119. S. Ito, T. Sagawa, Nat. Commun. 6, 7498 (2015)

    Article  Google Scholar 

  120. T. J. Kobayashi, Y. Sughiyama, Phys. Rev. Lett. 115, 238102 (2015)

    Article  Google Scholar 

  121. P. Sartori, S. Pigolotti, Phys. Rev. X 5, 041039 (2015)

    Google Scholar 

  122. T.E. Ouldridge, P.R. ten Wolde, Phys, Rev. Lett. 118, 158103 (2017)

    Article  Google Scholar 

  123. T.E. Ouldridge, C.C. Govern, P.R. ten Wolde, Phys, Rev. X 7, 021004 (2017)

    Google Scholar 

  124. T. Matsumoto, T. Sagawa, arXiv:1711.00264 (2017)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  127. M. Esposito, U. Harbola, S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009)

    Article  Google Scholar 

  128. T. Campisi, P. Hanggi, P. Talkner, Rev. Mod. Phys. 83, 771 (2011)

    Article  Google Scholar 

  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. À. M. Alhambra, L. Masanes, J. Oppenheim, C. Perry, Phys. Rev. X 6, 041017 (2016)

    Google Scholar 

  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/0301076

    Google Scholar 

  132. S.W. Kim, T. Sagawa, S. De Liberato, M. Ueda, Phys. Rev. Lett. 106, 070401 (2011)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  136. L. del Rio, J. Aberg, R. Renner, O. Dahlsten, V. Vedral, Nature 474, 61 (2011)

    Article  Google Scholar 

  137. K. Funo, Y. Watanabe, M. Ueda, Phys. Rev. E 88, 052121 (2013)

    Article  Google Scholar 

  138. H. Tajima, Phys. Rev. E 88, 042143 (2013)

    Article  Google Scholar 

  139. J.J. Park, K.-H. Kim, T. Sagawa, S.W. Kim, Phys. Rev. Lett. 111, 230402 (2013)

    Article  Google Scholar 

  140. J. Goold, M. Huber, A. Riera, L. del Rio, P. Skrzypzyk, J. Phys. A: Math. Theor. 49, 143001 (2016)

    Article  Google Scholar 

  141. M. Horodecki, J. Oppenheim, Nat. Commun. 4, 2059 (2013)

    Article  Google Scholar 

  142. F.G.S.L. Brandão, M. Horodecki, N.H.Y. Ng, J. Oppenheim, S. Wehner, Proc. Natl. Acad. Sci. 112, 3275 (2015)

    Article  Google Scholar 

  143. S. Popescu, A.J. Short, A. Winter, Nat. Phys. 2, 754–758 (2006)

    Article  Google Scholar 

  144. M. Rigol, V. Dunjko, M. Olshanii, Nature 452, 854–858 (2008)

    Article  Google Scholar 

  145. E. Iyoda, K. Kaneko, T. Sagawa, Phys. Rev. Lett. 119, 100601 (2017)

    Article  MathSciNet  Google Scholar 

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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.

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Authors and Affiliations

  1. Department of Applied Physics, The University of Tokyo, Tokyo, Japan

    Takahiro Sagawa

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  1. Takahiro Sagawa
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Editors and Affiliations

  1. Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana, USA

    Craig S. Lent

  2. Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana, USA

    Alexei O. Orlov

  3. Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana, USA

    Wolfgang Porod

  4. Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana, USA

    Gregory L. Snider

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Sagawa, T. (2019). Second Law, Entropy Production, and Reversibility in Thermodynamics of Information. In: Lent, C., Orlov, A., Porod, W., Snider, G. (eds) Energy Limits in Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-93458-7_3

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