  Molecular Dynamics is applied to Ferroelectric Perovskites in the framework
of a first-principles derived effective Hamiltonian (Zhong, Vanderbilt, Rabe,
Phys. Rev. Lett. {\bf 73} (1994), 1861). The degrees of freedom, that obey the
Newton equations of motion, are the local modes and the displacement modes. The
Nose-Hoover method is implemented, as well as the Parinello-Rahman scheme to
perform fixed temperature and fixed stress tensor simulations. This allows to
study the thermodynamics of ferroelectric perovskites and to reproduce
successfully the Monte Carlo results on phase transitions, polarization and
homogeneous strain evolution with temperature of BaTiO$_3$, taken as an
example.
