Entropy production from quasinormal modes

Horizons of black branes have an associated entropy current with non-negative divergence. We compute this divergence in a late-time transseries expansion for an inhomogeneous system evolving towards a maximally symmetric asymptotically anti-de Sitter black brane. The horizon area equilibrates on half the time-scale set by the dominant quasinormal mode and we find a simple analytic expression for this evolution purely in terms of the background and the quasinormal mode frequencies. This computation does not require a gradient expansion and is thus non-perturbative in momenta. We generalize this to include scalar and gauge field matter in any number of dimensions. Restricting to homogeneous evolution we match and prove earlier numerical work showing that the apparent horizon entropy saturates the area theorem, in that its time derivative periodically vanishes. The same is true for spherically symmetric evolution towards the Schwarzschild black hole.