  We study the stationary measures of Ginzburg-Landau (GL) stochastic processes
which describe the magnetization flux induced by the interaction with
reservoirs. To privilege simplicity to generality we restrict to quadratic
Hamiltonians where almost explicit formulas can be derived. We discuss the case
where reservoirs are represented by boundary generators (mathematical
reservoirs) and compare with more physical reservoirs made by large-infinite
systems.
  We prove the validity of the Fick law away from the boundaries.
  %and the existence of boundary layers for the mathematical reservoirs. We
also obtain in the context of the GL models a mathematical proof of the Darken
effect which shows uphill diffusion of carbon in specimen partly doped with the
addition of Si.
