  We compute the time evolution of the mutual information in out of equilibrium
quantum systems whose gravity duals are Vaidya spacetimes in three and four
dimensions, which describe the formation of a black hole through the collapse
of null dust. We find the holographic mutual information to be non monotonic in
time and always monogamous in the ranges explored. We also find that there is a
region in the configuration space where it vanishes at all times. We show that
the null energy condition is a necessary condition for both the strong
subadditivity of the holographic entanglement entropy and the monogamy of the
holographic mutual information.
