Energy fluctuations in vibrated and driven granular gases

TL;DR

This paper studies energy fluctuations in non-equilibrium granular gases, analyzing how inhomogeneities and velocity correlations affect the probability distribution of total energy, revealing Gaussian behavior in large systems.

Contribution

It provides an analytical approach to distinguish effects of spatial inhomogeneities and velocity correlations on energy fluctuations in granular gases.

Findings

Energy fluctuations are influenced by inhomogeneities and correlations.

The total energy distribution tends to Gaussian as system size increases.

Velocity correlations arise from inelastic collisions and affect energy statistics.

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 which have been previously observed numerically and which 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.