Hints of gravitational ergodicity: Berry’s ensemble and the universality of the semi-classical Page curve

Recent developments on black holes have shown that a unitarity-compatible Page curve can be obtained from an ensemble-averaged semi-classical approximation. In this paper, we emphasize (1) peculiar manifestation of unitarity is not specific to holes, and (2) it emerge single realization underlying unitary theory. To make things explicit, consider hard sphere gas leaking slowly small box into bigger box. This quantum chaotic system in which expect see the full description, while semi-classically, eigenstates are expected behave as though they live Berry's ensemble. We reproduce system, semi-classically. The computation has structural parallels replica wormholes, relies crucially ensemble averaging at each epoch, reveals interplay between multiple time-scales problem. Working with averaged $state$ rather than entanglement entropy, also engineer information "paradox". Our provides concrete example ergodic proxy for time average, explicit average over many theories. questions address here logically independent existence horizons, so gravity should viewed similar light.