  We show how to capture both the non-unitary Page curve and replica
wormhole-like contributions that restore unitarity in a toy quantum system with
random dynamics. The motivation is to find the simplest dynamical model that
captures this aspect of gravitational physics. In our model, we evolve with an
ensemble of Hamiltonians with GUE statistics within microcanonical windows. The
entropy of the averaged state gives the non-unitary curve, the averaged entropy
gives the unitary curve, and the difference comes from matrix index
contractions in the Haar averaging that connect the density matrices in a
replica wormhole-like manner.
