Title: Energy fluctuations in the steady uniform shear flow state of a granular gas

Abstract:
In the last years, Langevin-like equations describing the hydrodynamic
fluctuations of a homogeneous freely evolving granular gas have been
derived. They are a generalization of those introduced for molecular
fluids by Landau and Lifshitz.  The inelasticity of collisions induces
the presence of noise terms which are absent in molecular, elastic
fluids. Now, the theory is extended, without proof, to non-lineal
inhomogeneous states, by making two assumptions. The first one is that
the deterministic part of the fluctuating hydrodynamic equations can
be identified by linearizing the corresponding macroscopic equations
around the state being considering. The second assumption is that the
noise terms are just a local version of the expressions for the
homogeneous free state. Both hypothesis are based in results valid in
the elastic limit. As an application, the steady state reached by a
granular fluid under constant shear rate is considered and the
fluctuations of the total energy evaluated. The theoretical
predictions are compared with molecular dynamics simulation results. A
good agreement is observed. The relevance of taking into account
inherent rheological effects is discussed.