Geometric entropy, area, and strong subadditivity

TL;DR

This paper demonstrates that the area law for geometric entropy, related to black hole entropy, naturally follows from quantum mechanics and relativity principles, emphasizing the role of strong subadditivity.

Contribution

It provides a general derivation of the area law for geometric entropy using fundamental quantum and relativistic considerations, without relying on specific ultraviolet details.

Findings

The area law for geometric entropy is universally valid.

Strong subadditivity is key to deriving the area law.

The approach is based on basic quantum mechanics and relativity principles.

Abstract

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a density matrix with non zero entropy. This geometric entropy is believed to be deeply related to the entropy of black holes. Indeed, previous calculations in the context of quantum field theory, where the result is actually ultraviolet divergent, have shown that the geometric entropy is proportional to the area for a very special type of subsets. In this work we show that the area law follows in general from simple considerations based on quantum mechanics and relativity. An essential ingredient of our approach is the strong subadditive property of the quantum mechanical entropy.