  We argue that the usual notions of thermodynamic and entanglement entropy
have novel analogs in the context of higher spin theories. In particular, the
Wald and Ryu-Takayanagi formulas have natural higher spin extensions that we
work out and study. On the CFT side, just as standard entanglement entropy in
CFT_2 can be computed from twist field correlators, we demonstrate that by
introducing corresponding operators carrying higher spin charge we can
precisely reproduce our results from the bulk.
  We also show that the first law for entanglement entropy implies the
linearized field equations for the metric and higher spin fields, generalizing
recent work on deriving the linearized Einstein equations from the first law.
