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After a general overview of some features of the relaxation dynamics of theHamiltonian Mean Field model, its equilibrium thermodynamic properties are usedto 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 clusteredand a gaseous phases, whose existence could be associated to the largerelaxation times observed when $u_{1}<u<u_{c}$, with $u_{1}=0.5$. Starting fromthe hypothesis that the \textit{parametric resonance} is the microscopicmechanism allowing the energetic interchange between the particles during thecollisional regime, a phenomenological Fokker-Planck equation based on aLangevin equation with a multiplicative noise is proposed in order to describethe collisional relaxation of this system towards its final equilibrium, whichsupports the following dependence of the collisional relaxation timescale$\tau_{cr}=\tau_{0}N\equiv\sqrt{IN/g}$.

Remarks about the thermostatistical description of the HMF model Part II: Phenomenology of Relaxation Dynamics