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 to be easily verified.