About an H-theorem for systems with non-conservative interactions (Articolo in rivista)

Type
Label
  • About an H-theorem for systems with non-conservative interactions (Articolo in rivista) (literal)
Anno
  • 2013-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1088/1742-5468/2013/08/P08003 (literal)
Alternative label
  • Umberto Marini Bettolo Marconi (1); Andrea Puglisi (2); Angelo Vulpiani (2) (2013)
    About an H-theorem for systems with non-conservative interactions
    in Journal of statistical mechanics
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Umberto Marini Bettolo Marconi (1); Andrea Puglisi (2); Angelo Vulpiani (2) (literal)
Pagina inizio
  • P08003 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://iopscience.iop.org/1742-5468/2013/08/P08003/ (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 2013 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • August (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • (1) Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, I-62032, Camerino, INFN Perugia, Italy (2) CNR-ISC and Dipartimento di Fisica, Università La Sapienza, piazzale Aldo Moro 2, I-00185 Rome, Italy (literal)
Titolo
  • About an H-theorem for systems with non-conservative interactions (literal)
Abstract
  • We present some arguments in favor of an H-theorem for a generalization of the Boltzmann equation including non-conservative interactions and a linear Fokker-Planck-like thermostatting term. Such a non-linear equation describing the evolution of the single particle probability Pi(t) of being in state i at time t is a suitable model for granular gases and is referred to here as the Boltzmann-Fokker-Planck (BFP) equation. The conjectured H-functional, which appears to be non-increasing, is HC(t) = ?iPi(t)lnPi(t)/?i with ?i = limt??Pi(t), in analogy with the H-functional of Markov processes. The extension to continuous states is straightforward. A simple proof can be given for the elastic BFP equation. A semi-analytical proof is also offered for the BFP equation for so-called inelastic Maxwell molecules. Other evidence is obtained by solving particular BFP cases through numerical integration or through 'particle schemes' such as the direct simulation Monte Carlo. (literal)
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