  An alternative derivation of Brownian motion is presented. Instead of
supplementing the linearized Navier-Stokes equation with a fluctuating force,
we directly assume a Gaussian action functional for solvent velocity
fluctuations. Solvating a particle amounts to expelling the solvent and
prescribing a boundary condition to the solvent on the interface that is shared
with the solute. We study the dynamical effects of this boundary condition on
the solvent and derive explicit expressions for the solvent mean flow and
velocity correlations. Moreover, we show that the probability to observe
solvent velocity fluctuations that are compatible with the boundary condition
reproduces random Brownian motion of the solvated particle. We explicitly
calculate the translational and rotational diffusion coefficients of a
spherical particle using the presented formalism.
