  We express the entropy of a scalar field phi directly in terms of its
spacetime correlation function W(x,y) = <phi(x) phi(y)>, assuming that the
higher correlators are of "Gaussian" form. The resulting formula associates an
entropy S(R) to any spacetime region R; and when R is globally hyperbolic with
Cauchy surface Sigma, S(R) can be interpreted as the entropy of the reduced
density-matrix belonging to Sigma. One acquires in particular a new expression
for the entropy of entanglement across an event-horizon. Thanks to its
spacetime character, this expression makes sense in a causal set as well as in
a continuum spacetime.
