Anomalous Thermalization in Quantum Collective Models

We show that apparently thermalized states still store relevant amounts of information about their past, information that can be tracked by experiments involving nonequilibrium processes. We provide a condition for the microcanonical quantum Crook's theorem, and we test it by means of numerical experiments. In the Lipkin-Meshkov-Glick model, two different procedures leading to the same equilibrium states give rise to different statistics of work in nonequilibrium processes. In the Dicke model, two different trajectories for the same nonequilibrium protocol produce different statistics of work. Microcanonical averages provide the correct results for the expectation values of physical observables in all the cases; the microcanonical quantum Crook's theorem fails in some of them. We conclude that testing quantum fluctuation theorems is mandatory to verify if a system is properly thermalized.