Journal of Statistical Physics

, Volume 168, Issue 5, pp 1016–1030 | Cite as

Energy Statistics in Open Harmonic Networks

  • Tristan Benoist
  • Vojkan Jakšić
  • Claude-Alain Pillet


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).


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



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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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Tristan Benoist
    • 1
  • Vojkan Jakšić
    • 2
  • Claude-Alain Pillet
    • 3
  1. 1.Institut de Mathématiques de Toulouse, Équipe de Statistique et ProbabilitésUniversité Paul SabatierToulouse Cedex 9France
  2. 2.Department of Mathematics and StatisticsMcGill UniversityMontrealCanada
  3. 3.Aix Marseille UnivUniversité de Toulon, CNRS, CPTMarseilleFrance

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