  We show that a recently introduced stochastic thermostat [J. Chem. Phys. 126
(2007) 014101] can be considered as a global version of the Langevin
thermostat. We compare the global scheme and the local one (Langevin) from a
formal point of view and through practical calculations on a model
Lennard-Jones liquid. At variance with the local scheme, the global thermostat
preserves the dynamical properties for a wide range of coupling parameters, and
allows for a faster sampling of the phase-space.
