**Authors**: F. Bonetto, J.L. Lebowitz

**Title**: *Thermodynamic entropy production fluctuation in a
two dimensional shear flow model*

**Abstract:**
We investigate fluctuations in
the momentum flux across a surface perpendicular to the velocity
gradient in a stationary shear flow maintained by either thermostated
deterministic or by stochastic boundary conditions. In the
deterministic system the Gallavotti-Cohen (GC)relation for the
probability of large deviations, which holds for the phase space
volume contraction giving the Gibbs ensemble entropy production, never
seems to hold for the flux which gives the hydrodynamic entropy
production. In the stochastic case the GC relation is found to hold
for the total flux, as predicted by extensions of the GC theorem but
not for the flux across part of the surface. The latter appear to
satisfy a modified GC relation. Similar results are obtained for the
heat flux in a steady state produced by stochastic boundaries at
different temperatures.

**Key words: **Entropy production,
Nonequilibrium Statistical Mechanics