  Using a microfluidics device filled with a colloidal suspension of
microspheres, we test the laws of diffusion in the limit of small particle
numbers. Our focus is not just on average properties such as the mean flux, but
rather on the features of the entire distribution of allowed microscopic
trajectories that are possible during diffusive dynamics. The experiments show
that: (1) the flux distribution is Gaussian; (2) Fick's Law --- that the
average flux is proportional to the particle gradient --- holds even for
particle gradients down to one or zero particles; (3) the variance in the flux
is proportional to the sum of the particle numbers; and (4) there are backwards
flows, where particles flow up a concentration gradient, rather than down it,
and their numbers are well-predicted by theory and consistent with a new Flux
Fluctuation Theorem.

Statistical Mechanics;Soft Condensed Matter