Quantum mechanics and non-ordinary statistical mechanics

We argue that the de-coherence theory mimicking the occurrence of events in quantum mechanics does afford a satisfactory, albeit perhaps philosophically questionable, explanation of the emergence of classical mechanics, only in the case when both the system of interest and its environment fit conditions of ordinary statistical mechanics. In the case of anomalous statistical mechanics the de-coherence theory meets problems, and cannot maintain the promise of properly ensuring the transition to the classical regime. We examine the experimental case of intermittent fluorescence, with a non-Poisson distribution of waiting times in the "on" and "off" states, and we show that this anomalous condition becomes incompatible with the ordinary prescriptions of quantum statistical mechanics. We show that a possible way to address these issues rests on leaving the density perspective and on adopting the prescriptions of continuous random walk. We set for the advocates of de-coherence theory the challenge of reproducing these results from within a rigorously quantum Mechanical approach, with no events, and use of only unitary transformation.