Skip to main content

Energy Statistics in Open Harmonic Networks

Journal of Statistical Physics volume 168, pages 1016–1030 (2017)Cite this article

Abstract

We relate the large time asymptotics of the energy statistics in open harmonic networks to the variance-gamma distribution and prove a full large deviation principle. We consider both Hamiltonian and stochastic dynamics, the later case including electronic RC networks. We compare our theoretical predictions with the experimental data obtained by Ciliberto et al. (Phys. Rev. Lett. 110:180601, 2013).

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

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2

Notes

  1. The operator A acting on a Hilbert space is strictly positive whenever \(\langle \phi ,\,A\phi \rangle \ge \lambda \Vert \phi \Vert ^2\) for all \(\phi \) and some \(\lambda >0.\)

References

  1. Ciliberto, S., Imparato, A., Naert, A., Tanase, M.: Heat flux and entropy produced by thermal fluctuations. Phys. Rev. Lett. 110, 180601 (2013)

    ADS  Article  Google Scholar 

  2. Jakšić, V., Pillet, C.-A., Shirikyan, A.: Entropic fluctuations in thermally driven harmonic networks. J. Stat. Phys. 166, 926–1015 (2017)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. Jakšić, V., Pillet, C.-A., Shirikyan, A.: Entropic fluctuations in Gaussian dynamical systems. Rep. Math. Phys. 77, 335–376 (2016)

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. Lebowitz, J.L., Spohn, H.: Stationary non-equilibrium states of infinite harmonic systems. Commun. Math. Phys. 54, 97–120 (1977)

    ADS  MathSciNet  Article  Google Scholar 

  5. Watson, G.N.: A Treatise on the Theory of Bessel Functions, 2nd edn. Cambridge University Press, Cambridge (1966)

    MATH  Google Scholar 

Download references

Acknowledgements

We are grateful to Sergio Ciliberto and David Stephens for useful discussions. We also wish to thank Sergio Ciliberto for making available to us the raw data of the experiment reported in [1] which allowed one of us (T.B.) to analyze the data and plot the Fig. 2 in Sect. 4.3. The Research of T.B. was partly supported by ANR-11-LABX-0040-CIMI within the Program ANR-11-IDEX-0002-02 and by ANR Contract ANR-14-CE25-0003-0. The Research of V.J. was partly supported by NSERC. The work of C.-A.P. was partly funded by Excellence Initiative of Aix-Marseille University, A*MIDEX, a French “Investissements d’Avenir” Programme.

Author information

Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Équipe de Statistique et Probabilités, Université Paul Sabatier, 31062, Toulouse Cedex 9, France

    Tristan Benoist

  2. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada

    Vojkan Jakšić

  3. Aix Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France

    Claude-Alain Pillet

Authors
  1. Tristan Benoist
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vojkan Jakšić
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Claude-Alain Pillet
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vojkan Jakšić.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Benoist, T., Jakšić, V. & Pillet, CA. Energy Statistics in Open Harmonic Networks. J Stat Phys 168, 1016–1030 (2017). https://doi.org/10.1007/s10955-017-1842-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-017-1842-7

Keywords

  • Harmonic networks
  • Energy statistics
  • Open systems
  • Large deviations
  • Variance-gamma distribution