Abstract: There are 3 distimct set-ups for the weak coupling limit in the case of a small system interacting with a reservoir: starting from for the dynamics in the Heisenber picture, the Schrodinger picture and from the Liovillean. The first two are physically equivalent, they have been widely studied since at least the well known work of Davies. The third is not equivalent to the first and second and appears naturally in the study of return to equilibrium. Nevertheless, in the case of termal systems (and essentially only in this case), there is a simple relationship between all of them.