On Nernst's deduction of Planck's law and the problem of the Arnol'd diffusion

In a paper of the year 1916 Nernst attempted to understand the foundations of quantum mechanics without making recourse to energy discontinuities. In particular, in such a line of thought he gave two ''deductions'' of Planck's law, which, however, appear to escape a general understanding. In the present paper one of such deductions is explained. This fact appears to be not only of historical interest, because such a deduction is based on a dynamical hypothesis which is currently investigated in connection with the problem of the transition to stochasticity in systems of weakly coupled oscillators. (author)