Planckʹs formula and glassy behavior in classical nonequilibrium statistical mechanics

In statistical mechanics it is well known that one has to take into account the role of the relaxation times to equilibrium. We discuss the relevance of this fact for systems of weakly coupled harmonic oscillators in a classical framework, showing how one has a behavior similar to that of glassy systems and how one finds an analogue of Planckʹs formula. From this point of view, quantum equilibrium statistical mechanics thus appears as a first-order approximation in classical nonequilibrium statistical mechanics very far from equilibrium.