Average entanglement entropy at late times

The average entanglement entropy of a random pure state was determined by Page in 1993. Here we consider an isolated quantum system and study the behavior of the entanglement entropy at late times. We assume that the system is initially in a non-entangled state. We show that, for a random-matrix Hamiltonian, we recover the Page average and estimate the size of the fluctuations around the average. We derive also analogous results for random quadratic fermionic systems. The result is of interest for the analysis of thermalization in isolated quantum systems.