  The Sachdev-Ye-Kitaev (SYK$_{4}$) model has attracted attention for its fast
scrambling properties and its thermalization rate that is set only by the
temperature. In this work we ask the question of whether the SYK$_{4}$ model is
also a good thermal bath, in the sense that it allows a system coupled to it to
thermalize. We address this question by considering the dynamics of a system of
$N$ random non-interacting Majorana fermions coupled to an SYK$_{4}$ bath with
$M$ Majorana fermions that we solve with Keldysh techniques in the limit of
$M\gg N\gg 1$. We compare this nonequilibrium setting with a conventional bath
made of free non-interacting degrees of freedom with a continous spectrum. We
show that the SYK$_{4}$ bath is more efficient in thermalising the system at
weak coupling, due to its enhanced density of states at low frequency, while at
strong system-bath couplings both type of environments give rise to a similar
time scale for thermalisation.
