  We study reaction-diffusion processes with multi-species of particles and
hard-core interaction. We add boundary driving to the system by means of
external reservoirs which inject and remove particles, thus creating stationary
currents. We consider the condition that the time evolution of the average
occupation evolves as the discretized version of a system of coupled diffusive
equations with linear reactions. In particular, we identify a specific
one-parameter family of such linear reaction-diffusion systems where the
hydrodynamic limit behaviour can be obtained by means of a dual process. We
show that partial uphill diffusion is possible for the discrete particle
systems on the lattice, whereas it is lost in the hydrodynamic limit.
