Microcanonical Energy Sharing and a Page-like Curve for the Capacity of Entanglement

TL;DR

This paper investigates the capacity of entanglement in microcanonical ensembles, revealing it is governed by energy-sharing fluctuations and can be linked to thermal response data, illustrated through a toy model with a Page-like capacity curve.

Contribution

It introduces a microcanonical framework for understanding entanglement capacity, connecting it to thermal responses and energy sharing, with a novel Page-like capacity curve illustration.

Findings

Capacity is controlled by energy-sharing fluctuations.

Capacity can be expressed via thermal response data.

A toy model shows a Page-like capacity curve.

Abstract

We study the capacity of entanglement in the microcanonical ensemble for an effectively additive bipartite system. Using typicality and the block structure of the microcanonical reduced state, we show that in the thermodynamic regime the capacity is controlled by energy-sharing fluctuations and can be expressed purely in terms of standard thermal response data of the subsystems. As an illustration, we apply the result to a toy model consisting of a Schwarzian ``black-hole'' sector coupled to a two-dimensional CFT radiation sector. At fixed total energy, the growth of the radiation sector forces the common temperature to decrease, producing a smooth Page-like single-hump curve for the capacity. The construction is meant as a thermodynamic microcanonical mechanism for Page-like capacity curves, rather than as a complete dynamical evaporation calculation.