  We construct a collision model description of the thermalization of a finite
many-body system by using careful derivation of the corresponding Lindblad-type
master equation in the weak coupling regime. Using the example of two level
target system, we show that collision model thermalization is crucially
dependent on the various relevant system and bath timescales and on ensuring
that the environment is composed of ancillae which are resonant with the system
transition frequencies. Using this we extend our analysis to show that our
collision model can lead to thermalisation for certain classes of many-body
systems. We establish that for classically correlated systems our approach is
effective, while we also highlight its shortcomings, in particular with regards
to reaching entangled thermal states.
