Entropy, chaos and excited-state quantum phase transitions in the Dicke model

We study non-equilibrium 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. On the contrary, the heat dissipated by the process is affected neither by the onset of chaos, nor by the excited-state quantum phase transition.