Expressing entropy globally in terms of (4D) field-correlations

We have expressed the entropy of a scalar field directly in terms of its spacetime correlation function, assuming that the higher correlators are of "Gaussian" form. The resulting formula associates an entropy to any spacetime region, and when this region is globally hyperbolic with Cauchy surface then the entropy can be interpreted as the entropy of the reduced density-matrix belonging to the Cauchy surface. 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.