Out-of-Equilibrium Dynamics in Systems with Long-Range Interactions: Characterizing Quasi-stationary States

  • Pierre de Buyl
Part of the Springer Proceedings in Complexity book series (SPCOM)


Systems with long-range interactions (LRI) display unusual thermodynamical and dynamical properties that stem from the non-additive character of the interaction potential. We focus in this work on the lack of relaxation to thermal equilibrium when a LRI system is started out-of-equilibrium. Several attempts have been made at predicting the so-called quasi-stationary state (QSS) reached by the dynamics and at characterizing the resulting transition between magnetized and non-magnetized states. We review in this work recent theories and interpretations about the QSS. Several theories exist but none of them has provided yet a full account of the dynamics found in numerical simulations.


Vlasov equation Long-range interactions 



The author would like to acknowledge interesting discussions and collaborations with R. Bachelard, G. De Ninno, D. Fanelli, P. Gaspard, D. Mukamel and S. Ruffo.


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Pierre de Buyl
    • 1
  1. 1.Center for Complex Systems and Nonlinear PhenomenaUniversité libre de BruxellesBrusselsBelgium

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