We study nonequilibrium processes in an isolated quantum system-the Dicke model-focusing on the role played by the transition from integrability to chaos and the presence of excited-state quantum phase transitions. We show that both diagonal and entanglement entropies are abruptly increased by the onset of chaos. Also, this increase ends in both cases just after the system crosses the critical energy of the excited-state quantum phase transition. The link between entropy production, the development of chaos, and the excited-state quantum phase transition is more clear for the entanglement entropy.

We propose a protocol to prepare thermalized states storing relevant amounts of information about their past, and we study their resilience and the conditions under which we can profit from them. This protocol is based on the existence of an integrable stage in the preparation process, which makes it possible to record these amounts of information in the expected value of the corresponding integral of motion. By means of numerical calculations on the paradigmatic Dicke model, we show that it is possible to lead a quantum system onto a highly chaotic region, in which the eigenstate thermalization hypothesis is fulfilled and hence we find thermalization, without erasing this information. Notwithstanding, we also propose the existence of a quantum mechanism that mimics the high sensitivity to initial conditions trademark of classical chaos, and thus constitutes a powerful tool for information erasure. Its efficiency is rapidly increased with the number of particles, and hence the proposed protocol is only applicable to small quantum systems. It is induced by avoided level crossings in the transition from integrability to chaos, and it is switched on when the system goes through this transition with finite rapidity. We also show that the same mechanism contributes to hide this information from equilibrium measurements when the system follows the same path in the adiabatic limit.