Eur. Phys. J. B 51, 377-387 (2006)
https://doi.org/10.1140/epjb/e2006-00230-x

Energy fluctuations in vibrated and driven granular gases

¹ Laboratoire de Physique Théorique (CNRS UMR8627), Bâtiment 210, Université Paris-Sud, 91405 Orsay Cedex, France
² Laboratoire de Physique Théorique et Modèles Statistiques (CNRS UMR8626), Bâtiment 100, Université Paris-Sud, 91405 Orsay Cedex, France
³ Laboratoire Matière et Systèmes Complexes (CNRS UMR 7057), Université Denis Diderot (Paris VII), 2 place Jussieu, 75251 Paris Cedex 05, France
⁴ Center for Theoretical Biological Physics, UC San Diego 9500 Gilman Drive MC 0374, La Jolla, CA, 92093-0374, USA

Corresponding author: ^a Paolo.Visco@th.u-psud.fr

Received: 30 November 2005
Revised: 23 March 2006
Published online: 13 June 2006

Abstract

We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role. Interpreting the total kinetic energy as a sum of independent but not identically distributed random variables, it is possible to compute the probability density function (pdf) of the total energy. Neglecting correlations and using the analytical expression for the inhomogeneous temperature profile obtained from the granular hydrodynamic equations, we recover results that have previously been observed numerically and that had been attributed to the presence of correlations. In order to separate the effects of spatial inhomogeneities from those ascribable to velocity correlations, we have also considered two models of homogeneously thermostated gases: in this framework it is possible to reveal the presence of non-trivial effects due to velocity correlations between particles. Such correlations stem from the inelasticity of collisions. Moreover, the observation that the pdf of the total energy tends to a Gaussian in the large system limit suggests that they are also due to the finite size of the system.