Statistical theory of quasistationary states beyond the single water-bag case study

Malbor Asllani, Duccio Fanelli, Alessio Turchi, Timoteo Carletti, Xavier Leoncini

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An analytical solution for the out-of-equilibrium quasistationary states of the paradigmatic Hamiltonian mean field (HMF) model can be obtained from a maximum entropy principle. The theory has been so far tested with reference to a specific class of initial condition, the so called (single-level) water-bag type. In this paper a step forward is taken by considering an arbitrary number of overlapping water bags. The theory is benchmarked to direct microcanonical simulations performed for the case of a two-level water-bag. The comparison is shown to return an excellent agreement. © 2012 American Physical Society.

Original languageEnglish
Article number021148
Pages (from-to)021148
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2 Pt 1
Publication statusPublished - 2012


  • Hamiltonian Mean Field
  • quasi-stationary states
  • dynamical systems
  • long range interactions


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