  We consider general hamiltonian systems with quadratic interaction potential
and $N<\infty$ degrees of freedom, only $m$ of which have contact with external
world, that is subjected to damping and random stationary external forces. We
show that, as $t\to\infty$, already for $m=1$, the unique limiting distribution
exists for almost all interactions. Moreover, it is Gibbs if the external force
is the white noise, but typically not Gibbs for gaussian processes with smooth
trajectories. This conclusion survives also in the thermodynamic limit
$N\to\infty$.
