NCMC permits nonequilibrium relaxation of most of the system while part of the system is being driven over (or around) kinetic or energetic barriers prior to acceptance or rejection of the NCMC move. Instead of proposing large instantaneous perturbations to the system, NCMC divides a target large perturbation into a series of steps consisting of smaller instantaneous perturbations, where each perturbation is followed by propagated dynamics. After this series of perturbation and propagation steps, the whole sequence is accepted or rejected as an NCMC move. The intermediate states are always discarded and do not count towards any equilibrium averages or other properties as they are transiently out of equilibrium.