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Refined Second Law of Thermodynamics for Fast Random Processes

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Abstract

We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport and becomes relevant for processes far from quasi-stationary regime. General discussion is illustrated by numerical analysis of the optimal memory erasure protocol for a model for micron-size particle manipulated by optical tweezers.

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Acknowledgements

E.A. acknowledges support from the Academy of Finland as part of its Finland Distinguished Professor program, Project No. 129024. K.G. thanks S. Ciliberto, U. Seifert and C. Van den Broeck for inspiring discussions. His work was partly done within the framework of the STOSYMAP project ANR-11-BS01-015-02. R.M.’s work was partly supported by the OTARIE project ANR-07-BLAN-0235. P.M.-G. acknowledges support of the Center of Excellence “Analysis and Dynamics” of the Academy of Finland.

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Authors and Affiliations

  1. ACCESS Linnaeus Center, KTH, 10044, Stockholm, Sweden

    Erik Aurell

  2. Computational Biology Department, AlbaNova University Center, KTH, 10691, Stockholm, Sweden

    Erik Aurell

  3. Department of Information and Computer Science, Aalto University, PO Box 15400, 00076, Aalto, Finland

    Erik Aurell

  4. CNRS, Laboratoire de Physique, ENS Lyon, Université de Lyon, 46 Allée d’Italie, 69364, Lyon, France

    Krzysztof Gawȩdzki

  5. Laboratory of Physical Properties, Department of Rural Engineering, Technical University of Madrid, Avenida Complutense s/n, 28040, Madrid, Spain

    Carlos Mejía-Monasterio

  6. CNRS, Institut d’Astrophysique de Paris, Université Pierre et Marie Curie, 8 bis boulevard Arago, 75014, Paris, France

    Roya Mohayaee

  7. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 FIN-00014, Helsinki, Finland

    Paolo Muratore-Ginanneschi

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  1. Erik Aurell
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Correspondence to Krzysztof Gawȩdzki.

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Aurell, E., Gawȩdzki, K., Mejía-Monasterio, C. et al. Refined Second Law of Thermodynamics for Fast Random Processes. J Stat Phys 147, 487–505 (2012). https://doi.org/10.1007/s10955-012-0478-x

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