The framework of slowly evolving horizons is generalized to the case of black
branes in asymptotically anti-de Sitter spaces in arbitrary dimensions. The
results are used to analyze the behavior of both event and apparent horizons in
the gravity dual to boost-invariant flow. These considerations are motivated by
the fact that at second order in the gradient expansion the hydrodynamic
entropy current in the dual Yang-Mills theory appears to contain an ambiguity.
This ambiguity, in the case of boost-invariant flow, is linked with a similar
freedom on the gravity side. This leads to a phenomenological definition of the
entropy of black branes. Some insights on fluid/gravity duality and the
definition of entropy in a time-dependent setting are elucidated.Comment: RevTeX, 42 pages, 4 figure