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

This paper is the third one of a series of four. In the previous ones, we developed a thermodynamic and mechanical framework introducing the properties of the so-called Bernoulli oscillators. These last are classical oscillators submitted to an external force coming from the quantum vacuum, and driving a distinguished part of the oscillator motion itself which we call the hidden degree of freedom (HDF). In paper II, an expression for the HDF-potential effective in the classical expression of the mechanical energy theorem has been given. In order to show that this expression is consistent with a quantum mechanical context, a few unknown functions must be determined. To this purpose, we set up in this paper a mechanical-statistical framework for the system at hand. By investigating the properties of the reference statistical ensemble of oscillators we are able to find out the generalized state-equations needed in the expression of the mass-flow-theorem we have given in paper I. We produce the constitutive relations for the system pressure, (average) HDF-potential and other relevant statistical quantities. These expressions are for final comparison - to be performed in the following paper IV - with a wave-mechanical context. Discussion and physical interpretation of the framework here introduced are also provided.