  We provide a short proof for the exponential equivalence between misanthrope
processes in contact with weak reservoirs and those with impermeable
boundaries. As a consequence, we can derive both the hydrodynamic limit and the
large deviations of the totally asymmetric simple exclusion process (TASEP) in
contact with weak reservoirs. This extends a recent result which proved the
hydrodynamic behaviour of a vanishing viscocity approximation of the TASEP in
contact with weak reservoirs. Further applications to a class of asymmetric
exclusion processes with long jumps are discussed.
