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Universal features in the energetics of symmetry breaking

Nature Physics volume 10, pages 457–461 (2014)Cite this article

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Abstract

A breaking of symmetry involves an abrupt change in the set of microstates a system can explore. This change has unavoidable thermodynamic implications: a shrinkage of the microstate set results in an entropy decrease, which eventually needs to be compensated by heat dissipation and hence requires work. On the other hand, in a spontaneous symmetry breaking, the available phase-space volume changes without the need for work, yielding an apparent entropy decrease. Here we show that this entropy decrease is a key ingredient of a Szilard engine and Landauer’s principle, and perform a direct measurement of the entropy change along symmetry-breaking transitions for a Brownian particle subject to a bistable potential realized through two optical traps. The experiment confirms theoretical results based on fluctuation theorems, enables the construction of a Szilard engine extracting energy from a single thermal bath, and shows that a signature of a symmetry breaking in a system’s energetics is observable.

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Figure 1: Experimental protocol of symmetry breaking and symmetry restoration.
Figure 2: Energetics of symmetry breaking and symmetry restoration.
Figure 3: Experimental realization of the Szilard engine.

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Acknowledgements

I.A.M. and D.P. acknowledge financial support from the Fundació Privada Cellex Barcelona, Generalitat de Catalunya grant 2009-SGR-159, and from the Spanish Ministry of Science and Innovation (MICINN FIS2008-00114, FIS2011-24409). E.R. and J.M.R.P. acknowledge fruitful discussions with S. Grill, M. Jahnel, M. Behrndt, J. M. Horowitz and L. Dinís, and financial support from grants ENFASIS (Spanish Government) and MODELICO (Comunidad de Madrid). This article is dedicated to the memory of D. Petrov, leader of the Optical Tweezers group at ICFO, who passed away on 3 February 2014.

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Author notes

  1. É. Roldán and I. A. Martínez: These authors contributed equally to this work.

  2. D. Petrov: Deceased.

Authors and Affiliations

  1. Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense de Madrid, 28040 Madrid, Spain

    É. Roldán & J. M. R. Parrondo

  2. ICFO—Institut de Ciències Fotòniques, Mediterranean Technology Park, Av. Carl Friedrich Gauss, 3 08860 Castelldefels (Barcelona), Spain,

    I. A. Martínez & D. Petrov

  3. ICREA—Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys, 23, 08010 Barcelona, Spain

    D. Petrov

Authors
  1. É. Roldán
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  2. I. A. Martínez
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  3. J. M. R. Parrondo
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  4. D. Petrov
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Contributions

E.R. analysed experimental data, supported theoretical aspects and the design of the experiment, and performed computer simulations. I.A.M. designed the experiment, and obtained all experimental data. J.M.R.P. proposed and established the project, and developed its theoretical aspects. D.P. designed and supervised the experiment. All authors wrote the manuscript.

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Correspondence to J. M. R. Parrondo.

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The authors declare no competing financial interests.

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Roldán, É., Martínez, I., Parrondo, J. et al. Universal features in the energetics of symmetry breaking. Nature Phys 10, 457–461 (2014). https://doi.org/10.1038/nphys2940

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