F. Bonetto et Jl. Lebowitz, Thermodynamic entropy production fluctuation in a two-dimensional shear flow model - art. no. 056129, PHYS REV E, 6405(5), 2001, pp. 6129
We investigate fluctuations in the momentum flux across a surface perpendic
ular to the velocity gradient in a stationary shear flow maintained by eith
er thermostated deterministic or by stochastic boundary conditions. In the
deterministic system the fluctuation relation for the probability of large
deviations, which holds for the phase space volume contraction giving the G
ibbs ensemble entropy production, never seems to hold for the flux which gi
ves the hydrodynamic entropy production. In the stochastic case the fluctua
tion relation is found to hold for the total flux, as predicted by various
exact results, but not for the flux across part of the surface. The latter
appear to satisfy a modified fluctuation relation. Similar results are obta
ined for the heat flux in a steady state produced by stochastic boundaries
at different temperatures.