Energy Statistics in Open Harmonic Networks

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).

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Fig. 1
Fig. 2

Notes

  1. 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

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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.

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Correspondence to Vojkan Jakšić.

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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

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Keywords

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