# An Inverse Mass Expansion for the Mutual Information in Free Scalar QFT at Finite Temperature

## TL;DR

This paper investigates the mutual information and entanglement entropy in free scalar quantum field theories at finite temperature, revealing an area law behavior and a finite mutual information at infinite temperature due to classical correlations.

## Contribution

It introduces a perturbative inverse mass expansion for the mutual information in free scalar QFT at finite temperature, extending previous zero-temperature results.

## Key findings

- Mutual information remains finite at infinite temperature due to classical correlations.
- Both entanglement entropy and mutual information obey an area law at finite temperature.
- The area law coefficient is non-zero even at infinite temperature.

## Abstract

We study the entanglement entropy and the mutual information in coupled harmonic systems at finite temperature. Interestingly, we find that the mutual information does not vanish at infinite temperature, but it rather reaches a specific finite value, which can be attributed to classical correlations solely. We further obtain high and low temperature expansions for both quantities. Then, we extend the analysis performed in the seminal paper by Srednicki (Phys. Rev. Lett. 71, 666 (1993)) for free real scalar field theories in Minkowski space-time in 3+1 dimensions at a thermal state. We find that the mutual information obeys an area law, similar to that obeyed by the entanglement entropy at vanishing temperature. The coefficient of this area law does not vanish at infinite temperature. Then, we calculate this coefficient perturbatively in an $1/\mu$ expansion, where $\mu$ is the mass of the scalar field. Finally, we study the high and low temperature behaviour of the area law term.