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Experiments on the Thermodynamics of Information Processing

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Abstract

Thermodynamics explores laws of nature that govern processes of work, heat, matter, and information exchange between systems, subsystems, and their environments. It applies to all systems in nature, and it sets constraints on permissible physical processes, as formulated in four basic laws. Because of those fundamental laws, the total entropy in any process never decreases, which puts fundamental limits on the energy efficiency of heat engines, refrigerators, and computations. Although an awareness of the probabilistic nature of many processes in thermodynamics was present, experiments on such systems were traditionally based on macroscopic manipulations of many constituents and observations of their mean behavior. Here, I review the theory behind stochastic thermodynamics and related recent experiments.

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Notes

  1. 1.

    Cohen and Moerner use the name “Anti-Brownian ELectrokinetic,” or ABEL trap [10]. Because the trap can counteract all types of fluctuations, not just thermal ones, and because it can do so with forces that are not necessarily electrokinetic [11], we prefer the simpler and more general name of “feedback trap.”

  2. 2.

    The mutual information I measures or tells how much information memory contains about the system of interest.

  3. 3.

    For a spherical particle of radius r suspended in solution away from any boundary, the drag coefficient is given by the Stokes formula \(\gamma = 6 \pi \eta r\), where \(\eta \) is the viscosity of the surrounding fluid.

  4. 4.

    For an interval \(\Delta x\), Simpson’s rule is \(\int _x^{x+\Delta x} dx'\, f(x') \approx \Delta x \, \left[ \tfrac{1}{6} f(x) + \tfrac{4}{6} f(\frac{x+\Delta x}{2}) + \tfrac{1}{6} f(x+\right. \) \(\left. \Delta x)\right] \).

  5. 5.

    The definition of free energy difference here is between the final and the initial state \(\Delta F = F_\mathrm{final} - F_\mathrm{initial}.\)

  6. 6.

    Time reversal is just a mathematical abstraction. No experimentalist can reverse time and measure work while “undoing” the experiment. She or he can only run the reversed protocol forward in time and measure work, while assuming this to be equivalent to time reversal.

  7. 7.

    The asymptotic work W of a “reset” operation with success rate p is \( W = kT [ \ln (2) + p \ln (p) + (1- p )\ln (1-p)]\). See Chap. 8, where this formula is discussed.

References

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

    Google Scholar 

  2. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines. Rep. Prog. Phys. 75(126001), 1–58 (2012)

    Google Scholar 

  3. G.M. Wang, E.M. Sevick, E. Mittag, D.J. Searles, D.J. Evans, Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. Phys. Rev. Lett. 89, 050601 (2002)

    Article  ADS  Google Scholar 

  4. J. Liphardt, S. Dumont, S.B. Smith, I. Tinoco, C. Bustamante, Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski’s equality. Science 296(5574), 1832–1835 (2002)

    Google Scholar 

  5. S. Toyabe, T. Sagawa, M. Ueda, E. Muneyuki, M. Sano, Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality. Nat. Phys. 6, 988 (2010)

    Article  Google Scholar 

  6. J.V. Koski, V.F. Maisi, J.P. Pekola, D.V. Averin, Experimental realization of a Szilard engine with a single electron. PNAS 111, 13786–13789 (2014)

    Article  ADS  Google Scholar 

  7. A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, E. Lutz, Experimental verification of Landauer’s principle linking information and thermodynamics. Nature 483, 187–190 (2012)

    Article  ADS  Google Scholar 

  8. Y. Jun, J. Bechhoefer, Virtual potentials for feedback traps. Phys. Rev. E 86, 061106 (2012)

    Article  ADS  Google Scholar 

  9. R. Landauer, Irreversibility and heat generation in the computing process. IBM J. Res. Develop. 5, 183–191 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  10. A.E. Cohen, W.E. Moerner, Method for trapping and manipulating nanoscale objects in solution. Appl. Phys. Lett. 86, 093109 (2005)

    Article  ADS  Google Scholar 

  11. M.D. Armani, S.V. Chaudhary, R. Probst, B. Shapiro, Using feedback control of microflows to independently steer multiple particles. J. Microelectromech. Syst. 15, 945–956 (2006)

    Article  Google Scholar 

  12. A. Cho, One cool way to erase information. Science 332, 171 (2011)

    ADS  Google Scholar 

  13. M. Gavrilov, Y. Jun, J. Bechhoefer, Real-time calibration of a feedback trap. Rev. Sci. Instrum. 85(9) (2014)

    Google Scholar 

  14. Y. Jun, M. Gavrilov, J. Bechhoefer, High-precision test of Landauer’s principle in a feedback trap. Phys. Rev. Lett. 113, 190601 (2014)

    Article  ADS  Google Scholar 

  15. C.E. Shannon, A mathematical theory of communication. Bell Syst. Tech. J 27(3), 379–423 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  16. M. Gavrilov, J. Bechhoefer, Arbitrarily slow, non-quasistatic, isothermal transformations. EPL (Europhysics Letters) 114(5), 50002 (2016)

    Article  ADS  Google Scholar 

  17. M. Gavrilov, J. Koloczek, J. Bechhoefer, Feedback trap with scattering-based illumination, in Novel Techniques in Microscopy, page JT3A. 4. Opt. Soc. Am. (2015)

    Google Scholar 

  18. J.C. Maxwell, Theory of Heat (Green, and Co., Longmans, 1871)

    Google Scholar 

  19. Demon image. https://commons.wikimedia.org/wiki/File:Daemon-phk.png

  20. L. Szilard, On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings. Z. Physik 53, 840–856 (1929)

    Article  ADS  Google Scholar 

  21. L. Brillouin, Maxwell’s demon cannot operate: information and entropy. Int. J. Appl. Phys. 22(3), 334–337 (1951)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. H.S. Leff, A.F. Rex, Maxwell’s Demon 2: Entropy, Classical and Quantum Information (Computing, IOP, 2003)

    Google Scholar 

  23. C.H. Bennett, The thermodynamics of computation: a review. Int. J. Theor. Phys. 21, 905–940 (1982)

    Article  Google Scholar 

  24. O. Penrose, Foundations of Statistical Mechanics: A Deductive Treatment (Pergamon, 1970)

    Google Scholar 

  25. M.R. Juan, Parrondo. The Szilard engine revisited: Entropy, macroscopic randomness, and symmetry breaking phase transitions. Chaos 11(3), 725–733 (2001)

    Article  MATH  Google Scholar 

  26. J.M.R. Parrondo, J.M. Horowitz, T. Sagawa, Thermodynamics of information. Nat. Phys. (2015)

    Google Scholar 

  27. J. von Neumann, Theory of Self-Reproducing Automata (University of Illinois Press, Urbana, 1966)

    Google Scholar 

  28. C.H. Bennett, Logical reversibility of computation. IBM J. Res. Develop. 17, 525–532 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  29. T. Sagawa, M. Ueda, Minimal energy cost for thermodynamic information processing: measurement and information erasure. Phys. Rev. Lett. 102, 250602 (2009)

    Article  ADS  Google Scholar 

  30. T. Sagawa, Thermodynamic and logical reversibilities revisited. J. Stat. Mech., P03025 (2014)

    Google Scholar 

  31. J. Bechhoefer, Hidden Markov models for stochastic thermodynamics. New J. Phys. 17(7), 075003 (2015)

    Article  ADS  Google Scholar 

  32. C.-C. Shu, A. Chatterjee, G. Dunny, W.-S. Hu, D. Ramkrishna, Bistability versus bimodal distributions in gene regulatory processes from population balance. PLoS Comput. Biol. 7(8), 1–13, 08 (2011)

    Google Scholar 

  33. T. Sagawa, M. Ueda, Sagawa and Ueda reply. Phys. Rev. Lett. 104, 198904 (2010)

    Article  ADS  Google Scholar 

  34. T. Sagawa, M. Ueda, Information Thermodynamics: Maxwell’s Demon in Nonequilibrium Dynamics (Wiley-VCH, Weinheim, 2013)

    Google Scholar 

  35. D. Kondepudi, I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures (Wiley, CourseSmart Series, 2014)

    Book  MATH  Google Scholar 

  36. I. Prigogine, I. Stengers, Order Out of Chaos: Man’s New Dialogue with Nature. Flamingo edition (Bantam Books, 1984)

    Google Scholar 

  37. C. Van den Broeck, Stochastic thermodynamics, in Selforganization by Nonlinear Irreversible Processes: Proceedings of the Third International Conference Kühlungsborn, GDR, March 18–22, 1985, ed. by W. Ebeling, H. Ulbricht (Springer, Berlin, Heidelberg, 1986), pp. 57–61

    Chapter  Google Scholar 

  38. J. Schnakenberg, Network theory of microscopic and macroscopic behavior of master equation systems. Rev. Mod. Phys. 48, 571–585 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  39. X.-J. Zhang, H. Qian, M. Qian, Stochastic theory of nonequilibrium steady states and its applications. Part I. Phys. Rep. 510(1–2), 1–86 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  40. H. Ge, M. Qian, H. Qian, Stochastic theory of nonequilibrium steady states. Part II: applications in chemical biophysics. Phys. Rep. 510(3), 87–118 (2012)

    Article  ADS  Google Scholar 

  41. N.G. van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier Science, North-Holland Personal Library, 1992)

    MATH  Google Scholar 

  42. C.W. Gardiner, Stochastic Methods: A Handbook for the Natural and Social Sciences, 4th edn (Springer, 2009)

    Google Scholar 

  43. K. Sekimoto, Kinetic characterization of heat bath and the energetics of thermal ratchet models. J. Phys. Soc. Jpn. 66, 1234–1237 (1997)

    Article  ADS  Google Scholar 

  44. K. Sekimoto, Stochastic Energetics (Springer, 2010)

    Google Scholar 

  45. V. Blickle, T. Speck, L. Helden, U. Seifert, C. Bechinger, Thermodynamics of a colloidal particle in a time-dependent nonharmonic potential. Phys. Rev. Lett. 96, 070603 (2006)

    Article  ADS  Google Scholar 

  46. R. Klages, W. Just, C. Jarzynski, eds. Nonequilibrium Statistical Physics of Small Systems: Fluctuation Relations and Beyond (Wiley-VCH, 2013)

    Google Scholar 

  47. S. Blanes, F. Casas, A Concise Introduction to Geometric Numerical Integration (Chapman and Hall/CRC, 2016)

    Google Scholar 

  48. D.A. Sivak, J.D. Chodera, G.E. Crooks, Using nonequilibrium fluctuation theorems to understand and correct errors in equilibrium and nonequilibrium simulations of discrete Langevin dynamics. Phys. Rev. X 3, 011007 (2013)

    Google Scholar 

  49. M. Gavrilov, J. Bechhoefer, Feedback traps for virtual potentials. Philos. Trans. R. Soc. A 375, 20160217 (2017)

    Article  ADS  Google Scholar 

  50. C. Jarzynski, Nonequilibrium equality for free energy differences. Phys. Rev. Lett. 78, 2690–2693 (1997)

    Article  ADS  Google Scholar 

  51. C. Jarzynski, Rare events and the convergence of exponentially averaged work values. Phys. Rev. E 73, 046105 (2006)

    Article  ADS  Google Scholar 

  52. F. Douarche, S. Ciliberto, A. Petrosyan, I. Rabbiosi, An experimental test of the Jarzynski equality in a mechanical experiment. EPL (Europhysics Letters) 70(5), 593 (2005)

    Article  ADS  Google Scholar 

  53. N.C. Harris, Y. Song, C.-H. Kiang, Experimental free energy surface reconstruction from single-molecule force spectroscopy using Jarzynski’s equality. Phys. Rev. Lett. 99, 068101 (2007)

    Article  ADS  Google Scholar 

  54. A. Bérut, A. Petrosyan, S. Ciliberto, Detailed Jarzynski equality applied to a logically irreversible procedure. EPL 103, 60002 (2013)

    Article  Google Scholar 

  55. S. Luccioli, A. Imparato, A. Torcini, Free-energy landscape of mechanically unfolded model proteins: Extended Jarzinsky versus inherent structure reconstruction. Phys. Rev. E 78, 031907 (2008)

    Article  ADS  Google Scholar 

  56. A. Gupta, A. Vincent, K. Neupane, H. Yu, F. Wang, M.T. Woodside, Experimental validation of free-energy-landscape reconstruction from non-equilibrium single-molecule force spectroscopy measurements. Nat. Phys. 7(8), 631–634 (2011)

    Google Scholar 

  57. K. Sekimoto, S. Sasa, Complementarity relation for irreversible process derived from stochastic energetics. J. Phys. Soc. Jpn. 66(11), 3326–3328 (1997)

    Article  ADS  Google Scholar 

  58. É. Roldán, I.A. Martínez, J.M.R. Parrondo, D. Petrov, Universal features in the energetics of symmetry breaking. Nat. Phys. 10, 457–461 (2014)

    Article  Google Scholar 

  59. I.A. Martínez, É. Roldán, L. Dinis, D. Petrov, R.A. Rica, Adiabatic processes realized with a trapped Brownian particle. Phys. Rev. Lett. 114, 120601 (2015)

    Article  ADS  Google Scholar 

  60. V. Blickle, C. Bechinger, Realization of a micrometre-sized stochastic heat engine. Nat. Phys. 8(2), 143–146 (2012)

    Article  Google Scholar 

  61. J.V. Koski, T. Sagawa, O.-P. Saira, Y. Yoon, A. Kutvonen, P. Solinas, M. Mottonen, T. Ala-Nissila, J.P. Pekola, Distribution of entropy production in a single-electron box. Nat. Phys. 9(10), 644–648 (2013)

    Article  Google Scholar 

  62. J.V. Koski, V.F. Maisi, T. Sagawa, J.P. Pekola, Experimental observation of the role of mutual information in the nonequilibrium dynamics of a Maxwell demon. Phys. Rev. Lett. 113, 030601 (2014)

    Article  ADS  Google Scholar 

  63. J.V. Koski, A. Kutvonen, I.M. Khaymovich, T. Ala-Nissila, J.P. Pekola, On-chip Maxwell’s demon as an information-powered refrigerator. Phys. Rev. Lett. 115, 260602 (2015)

    Article  ADS  Google Scholar 

  64. J. Hong, B. Lambson, S. Dhuey, J. Bokor, Experimental test of Landauer’s principle in single-bit operations on nanomagnetic memory bits. Sci. Adv. 2, e1501492 (2016)

    Article  ADS  Google Scholar 

  65. L. Martini, M. Pancaldi, M. Madami, P. Vavassori, G. Gubbiotti, S. Tacchi, F. Hartmann, M. Emmerling, S. Höfling, L. Worschech, G. Carlotti, Experimental and theoretical analysis of Landauer erasure in nano-magnetic switches of different sizes. Nano Energy 19, 108–116 (2016)

    Article  Google Scholar 

  66. J.P.S. Peterson, R.S. Sarthour, A.M. Souza, I.S. Oliveira, J. Goold, K. Modi, D.O. Soares-Pinto, L.C. Céleri, Experimental demonstration of information to energy conversion in a quantum system at the Landauer limit. Proc. R. Soc. A 472, 2015.0813 (2016)

    Google Scholar 

  67. J. Roßnagel, S.T. Dawkins, K.N. Tolazzi, O. Abah, E. Lutz, F. Schmidt-Kaler, K. Singer, A single-atom heat engine. Science 352(6283), 325–329 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  68. M. Gavrilov, J. Bechhoefer, Erasure without work in an asymmetric, double-well potential. Phys. Rev. Lett. 117, 200601 (2016)

    Article  ADS  Google Scholar 

  69. K. Proesmans, Y. Dreher, M. Gavrilov, J. Bechhoefer, Christian Van den Broeck, Brownian duet: a novel tale of thermodynamic efficiency. Phys. Rev. X 6, 041010 (2016)

    Google Scholar 

  70. A. Ashkin, J.M. Dziedzic, J.E. Bjorkholm, S. Chu, Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11(5), 288–290 (1986)

    Article  ADS  Google Scholar 

  71. D. Collin, F. Ritort, C. Jarzynski, S.B. Smith, I. Tinoco, C. T. Bustamante, Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies. Nature (2005)

    Google Scholar 

  72. T.A. Waigh, Microrheology of complex fluids. Rep. Prog. Phys. 68(3), 685 (2005)

    Article  ADS  Google Scholar 

  73. S.P. Smith, S.R. Bhalotra, A.L. Brody, B.L. Brown, E.K. Boyda, M. Prentiss, Inexpensive optical tweezers for undergraduate laboratories. Am. J. Phys. 67(1), 26–35 (1999)

    Article  ADS  Google Scholar 

  74. J. Bechhoefer, S. Wilson, Faster, cheaper, safer optical tweezers for the undergraduate laboratory. Am. J. Phys. 70(4), 393–400 (2002)

    Article  ADS  Google Scholar 

  75. M.S. Rocha, Optical tweezers for undergraduates: theoretical analysis and experiments. Am. J. Phys 77(8), 704–712 (2009)

    Article  ADS  Google Scholar 

  76. T. Tlusty, A. Meller, R. Bar-Ziv, Optical gradient forces of strongly localized fields. Phys. Rev. Lett. 81, 1738–1741 (1998)

    Article  ADS  Google Scholar 

  77. A. Rohrbach, Stiffness of optical traps: Quantitative agreement between experiment and electromagnetic theory. Phys. Rev. Lett. 95, 168102 (2005)

    Article  ADS  Google Scholar 

  78. K. Berg-Sorensen, H. Flyvbjerg, Power spectrum analysis for optical tweezers. Rev. Sci. Instrum. 75(3), 594–612 (2004)

    Article  ADS  Google Scholar 

  79. K. Berg-Sorensen, E.J.G. Peterman, T. Weber, C.F. Schmidt, H. Flyvbjerg, Power spectrum analysis for optical tweezers. II: Laser wavelength dependence of parasitic filtering, and how to achieve high bandwidth. Rev. Sci. Instrum. 77(6) (2006)

    Google Scholar 

  80. C.A. Carlson, N.L. Sweeney, M.J. Nasse, J.C. Woehl, The corral trap: fabrication and software development. Proc. SPIE 7571, 757108–757108–6 (2010)

    Google Scholar 

  81. I.A. Martínez, É. Roldán, L. Dinis, D. Petrov, J.M.R. Parrondo, R.A. Rica, Brownian Carnot engine. Nat. Phys. 12(1), 67–70 (2016)

    Article  Google Scholar 

  82. M. Braun, A.P. Bregulla, K. Gunther, M. Mertig, F. Cichos, Single molecules trapped by dynamic inhomogeneous temperature fields. Nano Lett. 15(8), 5499–5505 (2015)

    Article  ADS  Google Scholar 

  83. A. Shenoy, M. Tanyeri, C.M. Schroeder, Characterizing the performance of the hydrodynamic trap using a control-based approach. Microfluid Nanofluid. 18(5), 1055–1066 (2015)

    Article  Google Scholar 

  84. B.R. Lutz, J. Chen, D.T. Schwartz, Hydrodynamic tweezers: noncontact trapping of single cells using steady streaming microeddies. Anal. Chem. 78(15), 5429–5435 (2006)

    Article  Google Scholar 

  85. C.M. Schroeder, E.S.G. Shaqfeh, S. Chu, Effect of hydrodynamic interactions on DNA dynamics in extensional flow: simulation and single molecule experiment. Macromolecules 37(24), 9242–9256 (2004)

    Google Scholar 

  86. M. Tanyeri, E.M. Johnson-Chavarria, C.M. Schroeder, Hydrodynamic trap for single particles and cells. Appl. Phys. Lett. 96(22) (2010)

    Google Scholar 

  87. M. Tanyeri, C.M. Schroeder, Manipulation and confinement of single particles using fluid flow. Nano Lett. 13(6), 2357–2364 (2013)

    Article  ADS  Google Scholar 

  88. K. Visscher, S.P. Gross, S.M. Block, Construction of multiple-beam optical traps with nanometer-resolution position sensing. IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076, 12 (1996)

    Google Scholar 

  89. M. Padgett, R. Di Leonardo, Holographic optical tweezers and their relevance to lab on chip devices. Lab Chip 11, 1196–1205 (2011)

    Article  Google Scholar 

  90. F. Ritort, Single-molecule experiments in biological physics: methods and applications. J. Phys. Condens. Matter 18(32), R531 (2006)

    Article  ADS  Google Scholar 

  91. G. Binnig, C.F. Quate, Ch. Gerber, Atomic force microscope. Phys. Rev. Lett. 56, 930–933 (1986)

    Article  ADS  Google Scholar 

  92. F.J. Giessibl, Advances in atomic force microscopy. Rev. Mod. Phys. 75, 949–983 (2003)

    Article  ADS  Google Scholar 

  93. M. Lopez-Suarez, I. Neri, L. Gammaitoni, Sub-k\(_B\)T micro-electromechanical irreversible logic gate. Nat. Commun. 7 (2016)

    Google Scholar 

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  1. Department of Biophysics and Biophysical Chemistry, Johns Hopkins University, Baltimore, MD, USA

    Momčilo Gavrilov

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Gavrilov, M. (2017). Introduction. In: Experiments on the Thermodynamics of Information Processing. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63694-8_1

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