Journal of Statistical Physics

, Volume 128, Issue 5, pp 1145–1152 | Cite as

Anomalous Dissipation in a Stochastically Forced Infinite-Dimensional System of Coupled Oscillators

  • Jonathan C. Mattingly
  • Toufic M. SuidanEmail author
  • Eric Vanden-Eijnden


We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure. This phenomenon, which has no finite dimensional equivalent, is due to the appearance of some anomalous dissipation mechanism which transports energy to infinity. This prevents the energy from building up locally and allows the system to converge to the invariant measure. The invariant measure is constructed explicitly and some of its properties are analyzed.


Invariant Measure Orthogonal Polynomial Covariance Structure Stat Phys Cantelli Lemma 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Jonathan C. Mattingly
    • 1
  • Toufic M. Suidan
    • 2
    Email author
  • Eric Vanden-Eijnden
    • 3
  1. 1.Duke UniversityDurhamUSA
  2. 2.University of CaliforniaSanta CruzUSA
  3. 3.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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