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

Abstract

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.

plainTeX, 14 pages, 2 figures. To appear in proceedings of ICGC2011, held Goa, Journal of Physics Conference Series. Most current version is available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/ (or wherever my home-page may be, such as http://www.physics.syr.edu/~sorkin/some.papers/)