Stellar dynamics and molecular dynamics : possible analogies

In stellar dynamics one is accostumed to deal with the Lynden--Bell distribution, which presents two peculiar characteristics: a) it resembles the quantum Fermi--Dirac distribution, and b) describes a state of metaequilibrium, that is expected to evolve on much longer time scales to a standard Maxwell--Boltzmann equilibrium. Here it is illustrated how an analogous situation seems to occur in molecular dynamics, described within the context of classical mechanics. The problem concerns the contribution of the internal degrees of freedom, typically the vibrations, to the specific heat; correspondingly, the metaequilibrium state leads to a Bose--Einstein--like rather than to a Fermi--Dirac--like distribution. We also point out that in molecular dynamics the ``nonclassical'' features seem to be related to the fact that the evolution of the energy is dominated by the presence of rare but conspicuous jumps, as in processes of L\'evy type; this too has some analogies with stellar dynamics.