Decoherence, wave-function collapses, non-ordinary statistical mechanics and the second principle

We show that the derivation of Lévy statistics from a Liouville‐like approach is still an unresolved problem, even though a satisfactory derivation resting on the Generalized Central Limit Theorem (GCLT) has been obtained. We discuss a quantum relaxation that according to the supposed equivalence between decoherence theory and wave function collapses is expected to be equivalent to the characteristic function of a Lévy process. We notice that this way of proceeding is equivalent to establishing a finite Kolmogorov‐Sinai (KS) entropy, and consequently, a condition compatible with the Second Principle of Thermodynamics even though the connection between this kind of entropy and the Clausius entropy is not yet known. The quantum treatment, based on density rather than the collapse‐induced symbolic sequences, conflicts with this conclusion.