  We first clarify through classical examples the status of the laws of
macroscopic physics as laws of large numbers. We next consider the mirrors
model in a finite $d$-dimensional domain and connected to particles reservoirs
at fixed chemical potentials. The dynamics is purely deterministic and
non-ergodic. We study the macroscopic current of particles in the stationary
regime. We show first that when the size of the system goes to infinity, the
behaviour of the stationary current of particles is governed by the proportion
of orbits crossing the system. This allows to formulate a necessary and
sufficient condition on the distribution of the set of orbits that ensures the
validity of Fick's law. Using this approach, we show that Fick's law relating
the stationary macroscopic current of particles to the concentration difference
holds in three dimensions and above. The negative correlations between crossing
orbits play a key role in the argument.
