  We study the effect of a non-vanishing chemical potential on the
thermalization time of a strongly coupled large $N_c$ gauge theory in
$(2+1)$-dimensions, using a specific bottom-up gravity model in asymptotically
AdS space. We first construct a perturbative solution to the gravity-equations,
which dynamically interpolates between two AdS black hole backgrounds with
different temperatures and chemical potentials, in a perturbative expansion of
a bulk neutral scalar field. In the dual field theory, this corresponds to a
quench dynamics by a marginal operator, where the corresponding coupling serves
as the small parameter in which the perturbation is carried out. The evolution
of non-local observables, such as the entanglement entropy, suggests that
thermalization time decreases with increasing chemical potential. We also
comment on the validity of our perturbative analysis.
