  We introduce a wide class of quantum maps that arise in collisional
reservoirs and are able to thermalize a system if they operate in conjunction
with an additional dephasing mechanism. These maps describe the effect of
collisions and induce transitions between populations that obey detailed
balance, but also create coherences that prevent the system from thermalizing.
We combine these maps with a unitary evolution acting during random Poissonian
times between collisions and causing dephasing. We find that, at a low
collision rate, the nontrivial combination of these two effects causes
thermalization in the system. This scenario is suitable for modeling
collisional reservoirs at equilibrium. We justify this claim by identifying the
conditions for such maps to arise within a scattering theory approach and
provide a thorough characterization of the resulting thermalization process.
