  There is presently considerable interest in accurately simulating the
evolution of open systems for which Markovian master equations fail. Examples
are systems that are time-dependent and/or strongly damped. A number of elegant
methods have now been devised to do this, but all use a bath consisting of a
continuum of harmonic oscillators. While this bath is clearly appropriate for,
e.g., systems coupled to the EM field, it is not so clear that it is a good
model for generic many-body systems. Here we explore a different approach to
exactly simulating open-systems: using a finite bath chosen to have certain key
properties of thermalizing many-body systems. To explore the numerical
resources required by this method to approximate an open system coupled to an
infinite bath, we simulate a weakly damped system and compare to the evolution
given by the relevant Markovian master equation. We obtain the Markovian
evolution with reasonable accuracy by using an additional averaging procedure,
and elucidate how the typicality of the bath generates the correct thermal
steady-state via the process of "eigenstate thermalization".
