Holographic evolution of the mutual information

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 con figuration 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.