  We consider a class of non-equilibrium pure states, which are generally
present in an isolated quantum statistical system. These are states of the form
$|\Psi\rangle=e^{-{\beta H \over 2}} U e^{{\beta H \over 2}} |\Psi_0\rangle$,
where $U$ is a unitary made out of simple operators and $|\Psi_0\rangle$ is a
typical equilibrium pure state with sharply peaked energy. We argue that in a
system with a holographic dual these states have a natural interpretation as an
AdS black hole with transient excitations behind the horizon. We explore the
interpretation of these states as pure states undergoing a time-dependent
spontaneous fluctuation out of equilibrium. While these states are atypical and
the microscopic phases of the wavefunction are correlated with the matrix
elements of simple operators, the states are partly disguised as equilibrium
states due to cancellations between contributions from different coarse-grained
energy bins. These cancellations are guaranteed by the KMS condition of the
underlying equilibrium state $|\Psi_0\rangle$. However, in correlators which
include the Hamiltonian $H$ these cancellations are spoiled and the
non-equilibrium nature of the state $|\Psi\rangle$ can be detected. We discuss
connections with the proposal that local observables behind the horizon are
realized as state-dependent operators. The states studied in this paper may be
useful for implementing an analogue of the "traversable wormhole" protocol for
a 1-sided black hole, which could potentially allow us to extract the
excitation from behind the horizon. We include some pedagogical background
material.
