Planck’s formula for classical oscillators with stochasticity thresholds

In this paper a further contribution is given to the attempt of understanding the consequences that occur in statistical mechanics from the hypothesis that there exist stochasticity thresholds in the dynamics of an oscillator weakly coupled to a conservative system of oscillators, following an old idea of Nernst. By taking a point of view due to Boltzmann, and identifying the thermodynamic energy with that fraction of mechanical energy which is highly unstable and thus available to thermal exchanges, it is shown how one is thus led to Planck’s formula.