  On the basis of analytical results and molecular dynamics simulations we
clarify the nonequilibrium dynamics of a long-range interacting system in
contact with a heat bath. For small couplings with the bath, we show that the
system can first be trapped in a Vlasov quasi-stationary state, then a
microcanonical one follows, and finally canonical equilibrium is reached at the
bath temperature. We compare a Langevin mesoscopic thermostat with Hamiltonian
reservoirs microscopically coupled with the system and demonstrate the
equivalence of the two descriptions. Our identification of the parameters
determining the quasi-stationary lifetimes could be exploited to control
experimental systems such as the Free Electron Laser, in the presence of
external noise or inherent imperfections.

Statistical Mechanics