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

Mallbor Assllani1,*, Duccio Fanelli2,3,†, Alessio Turchi3,4,5,‡, Timoteo Carletti6,§, and Xavier Leoncini5,∥

  • 1Dipartimento di Energetica, Universitá di Firenze, via Santa Marta, 3 - I-50139 Firenze, Italy
  • 2Dipartimento di Energetica, Universitá di Firenze, INFN and CNISM via Santa Marta, 3 - I-50139 Firenze, Italy
  • 3Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone, 1 - I-50019 Sesto Fiorentino, Italy
  • 4Dipartimento di Sistemi e Informatica, Universitá di Firenze,via Santa Marta, 3 - I-50139 Firenze, Italy
  • 5Centre de Physique théorique, Aix-Marseille Université, Campus de Luminy, F-13288 Marseille Cedex 09, France
  • 6naXys, Namur Center for Complex Systems and University of Namur, Namur BE-5000, Belgium

  • *malborasllani@yahoo.com
  • †duccio.fanelli@gmail.com
  • ‡alessio.turchi@gmail.com
  • §timoteo.carletti@fundp.ac.be
  • ∥xavier.leoncini@cpt.univ-mrs.fr
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Phys. Rev. E 85, 021148 – Published 27 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.021148

Abstract

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.

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Phys. Rev. E 85, 021148– Published 27 February, 2012
  • Received 29 September 2011

©2012 American Physical Society

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