  Quasistationary states are long-lived nonequilibrium states, observed in some
systems with long-range interactions under deterministic Hamiltonian evolution.
These intriguing non-Boltzmann states relax to equilibrium over times which
diverge algebraically with the system size. To test the robustness of this
phenomenon to non-deterministic dynamical processes, we have generalized the
paradigmatic model exhibiting such a behavior, the Hamiltonian Mean-Field
model, to include energy-conserving stochastic processes. Analysis, based on
the Boltzmann equation, a scaling approach and numerical studies, demonstrates
that in the long time limit, the system relaxes to the equilibrium state on
timescales which do not diverge algebraically with the system size. Thus,
quasistationarity takes place only as a crossover phenomenon on times
determined by the strength of the stochastic process.
