  We consider the entanglement entropy for holographic field theories in finite
volume. We show that the Araki-Lieb inequality is saturated for large enough
subregions, implying that the thermal entropy can be recovered from the
knowledge of the region and its complement. We observe that this actually is
forced upon us in holographic settings due to non-trivial features of the
causal wedges associated with a given boundary region. In the process, we
present an infinite set of extremal surfaces in Schwarzschild-AdS geometry
anchored on a given entangling surface. We also offer some speculations
regarding the homology constraint required for computing holographic
entanglement entropy.
