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Single-molecule measurement of the effective temperature in non-equilibrium steady states

Nature Physics volume 11, pages 971–977 (2015)Cite this article

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Abstract

Temperature is a well-defined quantity for systems in equilibrium. For glassy systems, it has been extended to the non-equilibrium regime, showing up as an effective quantity in a modified version of the fluctuation–dissipation theorem. However, experimental evidence supporting this definition remains scarce. Here, we present the first direct experimental demonstration of the effective temperature by measuring correlations and responses in single molecules in non-equilibrium steady states generated under external random forces. We combine experiment, analytical theory and simulations for systems with different levels of complexity, ranging from a single bead in an optical trap to two-state and multiple-state DNA hairpins. From these data, we extract a unifying picture for the existence of an effective temperature based on the relative order of various timescales characterizing intrinsic relaxation and external driving. Our study thus introduces driven small systems as a fertile ground to address fundamental concepts in statistical physics, condensed-matter physics and biophysics.

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Figure 1: Scheme of the stochastic driving.
Figure 2: Harmonic oscillator system.
Figure 3: Short hairpin systems.
Figure 4: Long hairpin system.

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Acknowledgements

F.R. is supported by an Institucio Catalana de Recerca i Estudis Avancats Academia 2013 grant. The research leading to these results (J.C.-S., M.R.-C., F.R.) has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under Grant 308850 INFERNOS (Information, Fluctuations, and Energy Control in Small Systems) and FIS2013-47796-P from the Spanish Research Council.

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Author notes

  1. E. Dieterich and J. Camunas-Soler: These authors contributed equally to this work.

Authors and Affiliations

  1. II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany,

    E. Dieterich & U. Seifert

  2. Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain,

    J. Camunas-Soler, M. Ribezzi-Crivellari & F. Ritort

  3. CIBER de Bioingeniería, Biomateriales y Nanomedicina, Instituto de Salud Carlos III, 28029 Madrid, Spain

    J. Camunas-Soler, M. Ribezzi-Crivellari & F. Ritort

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  1. E. Dieterich
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Contributions

F.R. and U.S. developed theory and designed experiments, E.D. performed theoretical calculations, simulations and data analysis, J.C.-S. and M.R.-C. performed the experiments. All authors contributed to writing the paper.

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Correspondence to F. Ritort.

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Dieterich, E., Camunas-Soler, J., Ribezzi-Crivellari, M. et al. Single-molecule measurement of the effective temperature in non-equilibrium steady states. Nature Phys 11, 971–977 (2015). https://doi.org/10.1038/nphys3435

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