  A general principle of statistical mechanics is that low energy excitations
of a thermal state change expectation values of observables by a very small
amount. However some observables in the vicinity of the horizon of a large
black hole in anti-de Sitter space naively seem to violate this bound. This
potential violation is related to the question of whether the black hole
interior can be described in AdS/CFT. Here we point out that if the possible
excitations are limited to those produced by a simple local source on the
boundary, and the possible observables are limited to products of field
operators in a single causal patch in the bulk, then these violations
disappear.
