Counting microstates of out-of-equilibrium black hole fluctuations

We construct and count the microstates of out-of-equilibrium eternal AdS black
holes in which a shell carrying an order one fraction of the black hole mass is emitted from the past horizon and re-absorbed at the future horizon. Our microstates have semiclassical interpretations in terms of matter propagating behind the horizon. We show that they span a Hilbert space with a dimension equal to the exponential of the horizon area of the intermediate black hole. This is consistent with the idea that, in a non-equilibrium setting, entropy is the logarithm of the number of microscopic configurations consistent with the dynamical macroscopic state. In our case, therefore, the entropy should measure the number of microstates consistent with a large and atypical macroscopic black hole fluctuation due to which part of the early time state becomes fully known to an external observer.