Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Large work extraction and the Landauer limit in a continuous Maxwell demon

Nature Physics volume 15, pages 660–664 (2019)Cite this article

Subjects

Abstract

The relation between entropy and information dates back to the classical Maxwell demon paradox1, a thought experiment proposed in 1867 by James Clerk Maxwell to violate the second law of thermodynamics. A variant of the classical Maxwell demon is the Szilard engine, proposed by Leo Szilard in 19291. In it, at a given time, the demon observes the compartment occupied by a single molecule in a vessel and extracts work by operating a pulley device. Here, we introduce the continuous Maxwell demon, a device capable of extracting arbitrarily large amounts of work per cycle by repeated measurements of the state of a system, and experimentally test it in single DNA hairpin pulling experiments. In the continuous Maxwell demon, the demon monitors the state of the DNA hairpin (folded or unfolded) by observing it at equally spaced time intervals, but it extracts work only when the molecule changes state. We demonstrate that the average maximum work per cycle that can be extracted by the continuous Maxwell demon is limited by the information content of the stored sequences, in agreement with the second law. Work extraction efficiency is found to be maximal in the large information-content limit where work extraction is fuelled by rare events.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Classical MD versus CMD.
Fig. 2: Single-molecule tests for the classical MD and CMD.
Fig. 3: Extracted work distributions.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the authors upon reasonable request.

References

  1. Leff, H. S. & Rex, A. F. (eds) Maxwell’s Demon: Entropy, Information, Computing (Adam Hilger, 1990).

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

    Article  MathSciNet  Google Scholar 

  3. Bennett, C. H. The thermodynamics of computation: a review. Int. J. Theor. Phys. 21, 905–940 (1983).

    Article  Google Scholar 

  4. Sagawa, T. & Ueda, M. Generalized Jarzynski equality under nonequilibrium feedback control. Phys. Rev. Lett. 104, 090602 (2010).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  6. Parrondo, J. M. R., Horowitz, J. M. & Sagawa, T. Thermodynamics of information. Nat. Phys. 11, 131–139 (2015).

    Article  Google Scholar 

  7. Seifert, U. Stochastic thermodynamics, fluctuation theorems, and molecular machines. Rep. Prog. Phys. 75, 126001 (2012).

    Article  ADS  Google Scholar 

  8. Ciliberto, S. Experiments in stochastic thermodynamics: short history and perspectives. Phys. Rev. X 7, 021051 (2017).

    Google Scholar 

  9. Toyabe, S., Sagawa, T., Ueda, M., Muneyuki, E. & Sano, M. Experimental demonstration of information-to-energy conversion and validation of the generalized Jarzynski equality. Nat. Phys. 6, 988–992 (2010).

    Article  Google Scholar 

  10. Berut, A. et al. Experimental verification of Landauer’s principle linking information and thermodynamics. Nature 483, 187–190 (2012).

    Article  ADS  Google Scholar 

  11. Mandal, D. & Jarzynski, C. Work and information processing in a solvable model of Maxwell’s demon. Proc. Natl Acad. Sci. USA 109, 11641–11645 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Koski, J. V., Maisi, V. F., Pekola, J. P. & Averin, D. V. Experimental realization of a Szilard engine with a single electron. Proc. Natl Acad. Sci. USA 111, 13786–13789 (2014).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Peterson, J. P. S. et al. Experimental demonstration of information to energy conversion in a quantum system at the Landauer limit. Proc. R. Soc. A 472, 20150813 (2016).

    Article  ADS  Google Scholar 

  17. Cover, T. M. & Thomas, J. A. Elements of Information Theory (Wiley, 1991).

  18. Verley, G., Esposito, M., Willaert, T. & Van den Broeck, C. The unlikely Carnot efficiency. Nat. Commun. 5, 4721 (2014).

    Article  ADS  Google Scholar 

  19. Garrahan, J. P. Aspects of non-equilibrium in classical and quantum systems: slow relaxation and glasses, large deviations, quantum non-ergodicity, and open quantum dynamics. Physica A 504, 130–154 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  20. Schreiber, T. Measuring information transfer. Phys. Rev. Lett. 85, 461–464 (2000).

    Article  ADS  Google Scholar 

  21. Horowitz, J. M. & Sandberg, H. Second-law-like inequalities with information and their interpretations. New J. Phys. 16, 125007 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  22. Horowitz, J. M. & Vaikuntanathan, S. Nonequilibrium detailed fluctuation theorem for repeated discrete feedback. Phys. Rev. E 82, 061120 (2010).

    Article  ADS  Google Scholar 

  23. Schmitt, R. K., Parrondo, J. M. R., Linke, H. & Johansson, J. Molecular motor efficiency is maximized in the presence of both power-stroke and rectification through feedback. New J. Phys. 17, 065011 (2015).

    Article  ADS  Google Scholar 

  24. Admon, T., Rahav, S. & Roichman, Y. Experimental realization of an information machine with tunable temporal correlations. Phys. Rev. Lett. 121, 180601 (2018).

    Article  ADS  Google Scholar 

  25. Pekola, J. P. Towards quantum thermodynamics in electronic circuits. Nat. Phys. 11, 118–123 (2015).

    Article  Google Scholar 

  26. Esposito, M., Harbola, U. & Mukamel, S. Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems. Rev. Mod. Phys. 81, 1665–1702 (2009).

  27. Ito, S. & Sagawa, T. Maxwell’s demon in biochemical signal transduction with feedback loop. Nat. Commun. 6, 7498 (2015).

    Article  ADS  Google Scholar 

  28. Bialek, W. Biophysics: Searching for Principles (Princeton Univ. Press, 2012).

  29. Huguet, J. M. et al. Single-molecule derivation of salt dependent base-pair free energies in DNA. Proc. Natl Acad. Sci. USA 107, 15431–15436 (2010).

    Article  ADS  Google Scholar 

  30. Camunas-Soler, J., Alemany, A. & Ritort, F. Experimental measurement of binding energy, selectivity, and allostery using fluctuation theorems. Science 355, 412–415 (2017).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge financial support from grants 308850 INFERNOS, 267862 MAGREPS (FP7 EU programme) FIS2013-47796-P, FIS2016-80458-P (Spanish Research Council) and ICREA Academia prize 2013 (Catalan government). M.R.-C. has received funding from the EU Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 749944.

Author information

Authors and Affiliations

  1. Condensed Matter Physics Department, University of Barcelona, Barcelona, Spain

    M. Ribezzi-Crivellari & F. Ritort

  2. Laboratoire de Biochimie, Institute of Chemistry, Biology and Innovation (CBI), UMR 8231, ESPCI Paris/CNRS, PSL Research University, Paris, France

    M. Ribezzi-Crivellari

  3. CIBER-BBN de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Sanidad Carlos III, Madrid, Spain

    F. Ritort

Authors
  1. M. Ribezzi-Crivellari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Ritort
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.R.-C. performed the experiments. F.R. performed the theoretical calculations. Both authors planned the research and contributed to data analysis and preparation of the manuscript.

Corresponding author

Correspondence to F. Ritort.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ribezzi-Crivellari, M., Ritort, F. Large work extraction and the Landauer limit in a continuous Maxwell demon. Nat. Phys. 15, 660–664 (2019). https://doi.org/10.1038/s41567-019-0481-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-019-0481-0

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing