Perturbations thermiques, fluctuations et approche à l'équilibre

An improved description of the thermodynamical equilibrium cannot leave out thermal perturbations and, generally speaking, some typical interactions affecting the system. Purposely we reformulate the basic, standard canonical ensemble apparatus for 1D oscillators distributing action quanta instead of energy. In this frame, describing action fluctuations by ±h/2 is also straightforward, and optimal match is found with our previous results. We show equivalence with quantum behaviour as the result of these fluctuations in presence of the modal constraint. The mean action and the Lagrange multiplier agree with an Oudet model and come out here as functions of temperature, quantum energy, quantum entropy. We define the thermodynamic potentials in the action domain and demonstrate a Bose-Einstein-like general distribution form holding for even strongly anharmonic oscillators (at least, with specific heat cv > 0). We extend previous definitions and computing of out-of-equilibrium entropy to the general anharmonic case where the cv value overcomes the classical estimate in agreement with the quantum model. As stated in previous work already, the thermal equilibrium condition is the equality between the quoted entropy difference across the fluctuation interval and the corresponding thermodynamical step. A simple view about the evolution to thermal equilibrium is given in the same framework.