  After a general overview of some features of the relaxation dynamics of the
Hamiltonian Mean Field model, its equilibrium thermodynamic properties are used
to rephrase the out-of-equilibrium regime for energies below the critical point
$u_{c}=0.75$ in terms of an effective dynamical coexistence between a clustered
and a gaseous phases, whose existence could be associated to the large
relaxation times observed when $u_{1}<u<u_{c}$, with $u_{1}=0.5$. Starting from
the hypothesis that the \textit{parametric resonance} is the microscopic
mechanism allowing the energetic interchange between the particles during the
collisional regime, a phenomenological Fokker-Planck equation based on a
Langevin equation with a multiplicative noise is proposed in order to describe
the collisional relaxation of this system towards its final equilibrium, which
supports the following dependence of the collisional relaxation timescale
$\tau_{cr}=\tau_{0}N\equiv\sqrt{IN/g}$.
