Violation of the Einstein relation in granular fluids: the role of correlations

Abstract

Abstract. We study the linear response in different models of driven granular gases. In some situations, even if the the velocity statistics can be strongly non-Gaussian, we do not observe appreciable violations of the Einstein formula for diffusion versus mobility. The situation changes when strong correlations between velocities and density are present: in this case, although a form of fluctuation-dissipation relation holds, the differential velocity response of a particle and its velocity self-correlation are no more proportional. This happens at high densities and strong inelasticities, but still in the fluid-like (and ergodic) regime.

Internal energy fluctuations of a granular gas under steady uniform shear flow

“…The work presented here must be clearly differentiated from other studies in which fluctuations of driven granular gases, in contact with some external energy source or thermal bath, have been considered [12][13][14]. The latter influences the stochastic properties of the granular gas in a nontrivial way and, consequently, it is not clear the relationship between fluctuations in granular systems with and without an external source of noise.…”

Fluctuating hydrodynamics for dilute granular gases

“…More specifically, they are not coupled to any external energy source or thermal bath, contrary to the driven granular gas models. For these models, the linear response to an external perturbation [23] as well as the validity of the Einstein relation [24] have been investigated by numerical simulations, and some empirical models have been proposed. It is not evident a direct relation between the free model considered here and the above driven models.…”

Role of Molecular Chaos in Granular Fluctuating Hydrodynamics

“…In granular systems, deviations from the white noise assumption are expected [5], but in the dilute case they are in general quite small (this is different in stationary dense systems, e.g. [32,36,34]). The most evident consequence of inelasticity is, instead, the variation of the dimensionless coefficient c in Eq.…”

“…The fluctuations obey, instead, a generalized Langevin equation where the noise has a variance which does not satisfy the FDR [14,3], and, in addition, is slightly colored. Note that the failure of FDR has also been observed in driven granular gases, but only at large packing fractions [32,36,34], while it is usually satisfied in the dilute case [31,1,33]. The theory in [5] makes use of the projection operator formalism and descends from a series of hypothesis, mainly the validity of Molecular Chaos and the Liouville equation for free particles undergoing hard core binary instantaneous collisions.…”