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

In a few previous papers, we developed a so-called classical fluctuation model providing (generalized) ''symmetrization rules '' - these make the classical expressions for energy transfer probabilities compliant with the detailed balance principle. For various physical processes, the symmetrized expressions of the transfer probabilities were shown to be remarkably improved - with respect to the performances of standard semiclassical models - in view of approaching quantum-mechanical results. Therefore, the possibility that a still undiscovered classical physics potential to describe quantum effects may be revealed by the model must be investigated. In this and a few next papers, we introduce some conceptual developments of the model and discuss the fundamental properties of the so-called Bernoulli oscillators (in the present paper I, the thermodynamic properties), whose behavior is analyzed in the light of the assumed existence of a ''hidden'' degree of freedom. The displayed properties are taken as a basis for a (proposed) classical interpretation of some quantum effects. As a final result, to be deployed in a last paper, a Newtonian-like equation of motion for ''quantum'' particles (uni-dimensional case) will be introduced, seeming to us the good candidate to set a bridge between classical and quantum physics. By these means - although we remain sometimes within the boundary of a conjectural framework, and limited to the case of translational motion - the possibility to approach a solution to the old problem of inconsistency between classical and quantum mechanics is displayed, and discussed as a proposal.