Propositional bases for the physics of the Bernoulli oscillators (A theory of the hidden degree of freedom) II. Mechanical framework

In a few previous papers, we developed a so-called classical fluctuation model, which revealed remarkably effectual in the task of approaching quantum mechanical results by the means of classical expressions. This paper is the second one of a series of four, introducing developments of the model. In paper I we provided some basic thermodynamic properties of the so-called Bernoulli oscillators: these are classical oscillators perturbed by the action of a ''hidden'' degree of freedom (HDF). In the present paper II, the mechanical properties corresponding to the thermodynamic model are investigated. HDF is identified physically as an oscillation superimposed to the particle classical degree of freedom. It is driven by an external, time-dependent force taking its origin in the quantum ''vacuum'', and is submitted to Heisenberg's principle as to a parametric constraint. The principle takes, in our framework, a peculiar classical-like interpretation. HDF perturbs the classical motion, so that an external (time-averaged) potential must be accounted for in the expression of the mechanical energy theorem. We give an analysis of the time-dependent forcing and a HDF-potential expression, as a function of an unknown parametric function whose identity will be made clear in the following paper IV. The HDF-potential is able to drive the particle throughout a barrier jump, thus providing us with a classical-like concept of the tunnelling phenomena. In some following papers, the discussed equations will be compared to both the contexts of our previous models and wave-mechanical physics.