Thermodynamics of the harmonic oscillator using coherent states

The ongoing discussion whether thermodynamic properties can be extracted fr om a (possibly approximate) quantum-mechanical time evolution using time av erages is fed with an instructive example. It is shown for the harmonic osc illator how the Hilbert space or an appropriately defined phase space must be populated in terms of coherent states in order to obtain the quantum res ult, respectively the classical one.