  We extend the results on decoherence in the thermodynamic limit [M. Frasca,
Phys. Lett. A {\bf 283}, 271 (2001)] to general Hamiltonians. It is shown that
N independent particles, initially properly prepared, have a set of observables
behaving classically in the thermodynamic limit. This particular set of
observables is then coupled to a quantum system that in this way decoheres so
to have the density matrix in a mixed form. This gives a proof of the
generality of this effect.
