  Classical systems placed in contact with a thermal bath will inevitably
equilibrate to a thermal state at the bath temperature. The same is not
generally true for open quantum systems, which place additional conditions on
the structure of the bath and system-bath interaction if thermalization is to
occur. Collisional models, or repeated interaction schemes, are a category of
microscopic open quantum system models that have seen growing use in studying
quantum thermalization, in which the bath is modeled as a large ensemble of
identical ancilla systems that sequentially interact with the system. We
demonstrate that, when each bath ancilla is prepared in a thermal state with a
discrete spectrum that matches the energy eigenstate transitions of the system,
the system dynamics generated by the collisional model framework are identical
to those generated under the Metropolis algorithm. This equivalence holds not
just in the steady state regime, but also in the transient regime. As the
Metropolis scheme does not require explicitly modeling the system-bath
interaction, this allows it to be used as a computationally efficient
alternative for simulating collisional model dynamics.
