  We study the dynamical features of Maggiore's generalised commutation
relations. We focus on their generality and, in particular, their dependence on
the Hamiltonian H. We derive the generalisation of the Planck's law for black
body spectrum, study the statistical mechanics of free particles, and study the
early universe evolution which now exhibits non trivial features. We find that
the dynamical features, found here and in our earlier work, are all generic and
vary systematically with respect to the asymptotic growth of the Hamiltonian H.
