A Comment on Entropy and Area

TL;DR

This paper demonstrates the equivalence of entanglement entropy and thermal entropy for quantum fields near a boundary, suggesting a classical entropy interpretation via the Bekenstein--Hawking formula.

Contribution

It establishes the equivalence of entanglement and thermal density matrices for quantum fields with boundaries, linking quantum entanglement to classical black hole entropy.

Findings

Entanglement entropy equals thermal entropy in Rindler space.

Density matrices describing vacuum and thermal states are identical.

Boundary entropy may be interpreted via the Bekenstein--Hawking formula.

Abstract

For an arbitrary quantum field in flat space with a planar boundary, an entropy of entanglement, associated with correlations across the boundary, is present when the field is in its vacuum state. The vacuum state of the same quantum field appears thermal in Rindler space, with an associated thermal entropy. We show that the density matrices describing the two situations are identical, and therefore that the two entropies are equal. We comment on the generality and significance of this result, and make use of it in analyzing the area and cutoff dependence of the entropy. The equivalence of the density matrices leads us to speculate that a planar boundary in Minkowski space has a classical entropy given by the Bekenstein--Hawking formula.