Perturbative Method for Mutual Information and Thermal Entropy of Scalar Quantum Fields

TL;DR

This paper introduces a perturbative method to compute mutual information and thermal entropy of massless scalar quantum fields, providing all-order expansions in the ratio of region size to separation and small temperature limit.

Contribution

It presents a novel perturbative approach based on skewed correlation matrices to calculate quantum field entropies and mutual information for disjoint regions.

Findings

Mutual information expansion to all orders in r/R.

Perturbative expansion of thermal entropy difference at low temperatures.

Applicable to massless scalar quantum fields.

Abstract

A new approach is presented to compute entropy for massless scalar quantum fields. By perturbing a skewed correlation matrix composed of field operator correlation functions, the mutual information is obtained for disjoint spherical regions of size $r$ at separation $R$, including an expansion to all orders in $r/R$. This approach also permits a perturbative expansion for the thermal field entropy difference in the small temperature limit ($T \ll 1/r$).