caa a22 4500 467892962 CHVBK 20180406152754.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s10955-006-9161-4 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9161-4 Fluctuations of Power Injection in Randomly Driven Granular Gases [Elektronische Daten] [Paolo Visco, Andrea Puglisi, Alain Barrat, Emmanuel Trizac, Frédéric van Wijland] We investigate the large deviation function π∞(w) for the fluctuations of the power W(t) = wt, integrated over a time t, injected by a homogeneous random driving into a granular gas, in the infinite time limit. Our analytical study starts from a generalized Liouville equation and exploits a Molecular Chaos-like assumption. We obtain an equation for the generating function of the cumulants μ(λ) which appears as a generalization of the inelastic Boltzmann equation and has a clear physical interpretation. Reasonable assumptions are used to obtain μ(λ) in a closed analytical form. A Legendre transform is sufficient to get the large deviation function π∞(w). Our main result, apart from an estimate of all the cumulants of W(t) at large times t, is that π∞ has no negative branch. This immediately results in the inapplicability of the Gallavotti-Cohen Fluctuation Relation (GCFR), that in previous studies had been suggested to be valid for injected power in driven granular gases. We also present numerical results, in order to discuss the finite time behavior of the fluctuations of W (t) . We discover that their probability density function converges extremely slowly to its asymptotic scaling form: the third cumulant saturates after a characteristic time τ larger than ∼50 mean free times and the higher order cumulants evolve even slower. The asymptotic value is in good agreement with our theory. Remarkably, a numerical check of the GCFR is feasible only at small times (at most τ/10), since negative events disappear at larger times. At such small times this check leads to the misleading conclusion that GCFR is satisfied for π∞(w). We offer an explanation for this remarkable apparent verification. In the inelastic Maxwell model, where a better statistics can be achieved, we are able to numerically observe the "failure” of GCFR. Springer Science + Business Media, Inc., 2006 Granular gases nationallicence nonequilibrium steady-states nationallicence large deviation nationallicence fluctuation-dissipation nationallicence Visco Paolo Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405, Orsay cedex, France aut Puglisi Andrea Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405, Orsay cedex, France aut Barrat Alain Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405, Orsay cedex, France aut Trizac Emmanuel Laboratoire de Physique Théorique et Modèles Statistiques (CNRS UMR 8626), Bâtiment 100, Université Paris-Sud, 91405, Orsay cedex, France aut van Wijland Frédéric Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405, Orsay cedex, France aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/3(2006-11-01), 533-568 0022-4715 125:3<533 2006 125 10955 https://doi.org/10.1007/s10955-006-9161-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9161-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Visco Paolo Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405, Orsay cedex, France aut NATIONALLICENCE 700 1- Puglisi Andrea Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405, Orsay cedex, France aut NATIONALLICENCE 700 1- Barrat Alain Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405, Orsay cedex, France aut NATIONALLICENCE 700 1- Trizac Emmanuel Laboratoire de Physique Théorique et Modèles Statistiques (CNRS UMR 8626), Bâtiment 100, Université Paris-Sud, 91405, Orsay cedex, France aut NATIONALLICENCE 700 1- van Wijland Frédéric Laboratoire de Physique Théorique (CNRS UMR 8627), Bâtiment 210, Université Paris-Sud, 91405, Orsay cedex, France aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 125/3(2006-11-01), 533-568 0022-4715 125:3<533 2006 125 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer