Abstract

The Carnot cycle imposes a fundamental upper limit to the efficiency of a macroscopic motor operating between two thermal baths1. However, this bound needs to be reinterpreted at microscopic scales, where molecular bio-motors2 and some artificial micro-engines3,4,5 operate. As described by stochastic thermodynamics6,7, energy transfers in microscopic systems are random and thermal fluctuations induce transient decreases of entropy, allowing for possible violations of the Carnot limit8. Here we report an experimental realization of a Carnot engine with a single optically trapped Brownian particle as the working substance. We present an exhaustive study of the energetics of the engine and analyse the fluctuations of the finite-time efficiency, showing that the Carnot bound can be surpassed for a small number of non-equilibrium cycles. As its macroscopic counterpart, the energetics of our Carnot device exhibits basic properties that one would expect to observe in any microscopic energy transducer operating with baths at different temperatures9,10,11. Our results characterize the sources of irreversibility in the engine and the statistical properties of the efficiency—an insight that could inspire new strategies in the design of efficient nano-motors.

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Acknowledgements

I.A.M., É.R., D.P. and R.A.R. acknowledge financial support from Fundació Privada Cellex Barcelona. I.A.M., D.P. and R.A.R. acknowledge financial support from grant NanoMQ (FIS2011-24409, MINECO). I.A.M. acknowledges financial support from the European Research Council Grant OUTEFLUCOP. É.R., L.D. and J.M.R.P. acknowledge financial support from grant ENFASIS (FIS2011-22644, MINECO) and TerMic (FIS2014-52486-R, MINECO). We wish to acknowledge the work of S. Corcuff at the earliest stage of the project and fruitful discussions with R. Brito. D. Petrov passed away on 3 February 2014. He initiated the development of this project while he was the leader of the Optical Tweezers group at ICFO. We mourn the loss of a great colleague and friend.

Author information

Author notes

    • I. A. Martínez
    •  & É. Roldán

    These authors contributed equally to this work.

Affiliations

  1. ICFO-Institut de Ciències Fotòniques, Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain

    • I. A. Martínez
    • , É. Roldán
    • , D. Petrov
    •  & R. A. Rica
  2. Laboratoire de Physique, École Normale Supérieure, CNRS UMR5672 46 Allée d’Italie, 69364 Lyon, France

    • I. A. Martínez
  3. Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38 01187 Dresden, Germany

    • É. Roldán
  4. GISC-Grupo Interdisciplinar de Sistemas Complejos, 28040 Madrid, Spain

    • É. Roldán
    • , L. Dinis
    •  & J. M. R. Parrondo
  5. Departamento de Fisica Atómica, Molecular y Nuclear, Universidad Complutense Madrid, 28040 Madrid, Spain

    • L. Dinis
    •  & J. M. R. Parrondo

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Contributions

I.A.M. designed the experiment, obtained all experimental data and analysed experimental data. É.R. designed the experiment, analysed experimental data and supported theoretical aspects. L.D. supported theoretical aspects. D.P. proposed and established the project, and supervised the experiment. J.M.R.P. proposed and established the project and developed its theoretical aspects. R.A.R. supported and supervised the experiment. All authors discussed the results and wrote the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to I. A. Martínez or É. Roldán or R. A. Rica.

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DOI

https://doi.org/10.1038/nphys3518

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