  The entanglement entropy of a free quantum field in a coherent state is
independent of its stress energy content. We use this result to highlight the
fact that while the Einstein equations for first order variations about a
locally maximally symmetric vacuum state of geometry and quantum fields seem to
follow from Jacobson's principle of maximal vacuum entanglement entropy, their
possible derivation from this principle for the physically relevant case of
finite but small variations remains an open issue. We also apply this result to
the context of Bianchi's identification, independent of unknown Planck scale
physics, of the first order variation of Bekenstein Hawking area with that of
vacuum entanglement entropy. We argue that under certain technical assumptions
this identification seems not to be extendible to the context of finite but
small variations to coherent states. Our particular method of estimation of
entanglement entropy variation reveals the existence of certain contributions
over and above those appearing in Jacobson's and Bianchi's works. We discuss
the sense in which these contributions may be subleading to those already
present in these works.
