Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension

A dispersive medium becomes entangled with zero-point fluctuations in the
vacuum. We consider an arbitrary array of material bodies weakly interacting
with a quantum field and compute the quantum mutual information between them.
It is shown that the mutual information in D dimensions can be mapped to
classical thermodynamic entropy in D+1 dimensions. As a specific example, we
compute the mutual information both analytically and numerically for a range of
separation distances between two bodies in D=2 dimensions and find a
logarithmic correction to the area law at short separations. A key advantage of
our method is that it allows the strong subadditivity property---notoriously
difficult to prove for quantum systems---to be easily verified.