  A nonequilibrium fluctuation theorem is established for a colloidal particle
driven by an external force within the hydrodynamic theory of Brownian motion,
describing hydrodynamic memory effects such as the t^(-3/2) power-law decay of
the velocity autocorrelation function. The generalized Langevin equation is
obtained for the general case of slip boundary conditions between the particle
and the fluid. The Gaussian probability distributions for the particle to
evolve in position-velocity space are deduced. It is proved that the joint
probability distributions of forward and time-reversed paths have a ratio
depending only on the work performed by the external force and the fluid
temperature, in spite of the nonMarkovian character of the generalized Langevin
process.
