  We compare simulations performed using the Nos\'e-Hoover and the Langevin
thermostats with the Hamiltonian dynamics of a long-range interacting system in
contact with a reservoir. We find that while the statistical mechanics
equilibrium properties of the system are recovered by all the different
methods, the Nos\'e-Hoover and the Langevin thermostats fail in reproducing the
nonequilibrium behavior of such Hamiltonian.
