  Long-range interacting systems, while relaxing towards equilibrium, may get
trapped in nonequilibrium quasistationary states (QSS) for a time which
diverges algebraically with the system size. These intriguing non-Boltzmann
states have been observed under deterministic Hamiltonian evolution of a
paradigmatic system, the Hamiltonian Mean-Field (HMF) model. We study here the
robustness of QSS with respect to stochastic processes beyond deterministic
dynamics within a microcanonical ensemble. To this end, we generalize the HMF
model by allowing for stochastic three-particle collision dynamics in addition
to the deterministic ones. By analyzing the resulting Boltzmann equation for
the phase space density, we demonstrate that in the presence of stochasticity,
QSS occur only as a crossover phenomenon over a finite time determined by the
strength of the stochastic process. In particular, we argue that the relaxation
time to equilibrium does not scale algebraically with the system size. We
propose a scaling form for the relaxation time which is in very good agreement
with results of extensive numerical simulations. The broader validity of these
results is tested on a different stochastic HMF model involving microcanonical
Monte Carlo dynamical moves.
