Thermal and chemical response from entanglement entropy

TL;DR

This paper demonstrates that in large subregions of interacting quantum field theories at finite density, the derivative of entanglement entropy approaches thermal entropy density, linking entanglement properties to thermodynamic behavior.

Contribution

It establishes a universal relation between entanglement entropy derivatives and thermal entropy density in continuum QFTs, supported by nonperturbative evidence in the O(4) model.

Findings

Derivative of EE approaches thermal entropy density in large regions.

EE satisfies thermodynamic response relations at finite chemical potential.

Evidence from the O(4) model supports the universality of these relations.

Abstract

We study entanglement entropy (EE) in interacting quantum field theories (QFTs) at finite density. We argue that, in the limit of large subregions, the derivative of EE with respect to the size of the entangling region approaches the thermal entropy density, independently of microscopic details. We make this relation explicit using slab-shaped subregions, where the limiting behavior can be directly identified. At finite chemical potential, we show that EE satisfies thermodynamic response relations, including a generalized Maxwell relation linking chemical potential and charge density. We provide strong nonperturbative evidence for these statements in the three-dimensional $\operatorname{O}\left(4\right)$ model, and conjecture that they are generic features of continuum QFTs, establishing a two-way link between entanglement and thermodynamics that opens a route toward extracting the equation-of-state information from entanglement data.