We study the contribution of advection by thermal velocity fluctuations to
the effective diffusion coefficient in a mixture of two indistinguishable
fluids. The enhancement of the diffusive transport depends on the system size L
and grows as \ln(L/L_0) in quasi two-dimensional systems, while in three
dimensions it scales as L_0^{-1}-L^{-1}, where L_0 is a reference length. The
predictions of a simple fluctuating hydrodynamics theory are compared to
results from particle simulations and a finite-volume solver and excellent
agreement is observed. Our results conclusively demonstrate that the nonlinear
advective terms need to be retained in the equations of fluctuating
hydrodynamics when modeling transport in small-scale finite systems.Comment: To appear in Phys. Rev. Lett., 201