  We study the short-distance structure of geometric entanglement entropy in
certain theories with a built-in scale of nonlocality. In particular we examine
the cases of Little String Theory and Noncommutative Yang-Mills theory, using
their AdS/CFT descriptions. We compute the entanglement entropy via the
holographic ansatz of Ryu and Takayanagi to conclude that the area law is
violated at distance scales that sample the nonlocality of these models, being
replaced by an extensive volume law. In the case of the noncommutative model,
the critical length scale that reveals the area/volume law transition is
strongly affected by UV/IR mixing effects. We also present an argument showing
that Lorentz symmetry tends to protect the area law for theories with
field-theoretical density of states.
