Analog of Planck's formula and effective temperature in classical statistical mechanics far from equilibrium

We study the statistical mechanics very far from equilibrium for a classica l system of harmonic oscillators colliding with point particles (mimicking a heat reservoir), for negligible initial energies of the oscillators. It i s known that for high frequencies the times of relaxation to equilibrium ar e extremely long, so that one meets with situations of quasiequilibrium ver y far from equilibrium similar to those of glassy systems. Using recent res ults from the theory of dynamical systems, we deduce a functional relation between energy variance and mean energy that was introduced by Einstein phe nomenologically in connection with Planck's formula. It is then discussed h ow this leads to an analog of Planck's formula. This requires using Einstei n's relation between specific heat and energy variance to define an effecti ve temperature in a context of quasiequilibrium far from equilibrium, as is familiar for glassy systems.