Entanglement entropy and the first law at third order for boosted black branes

TL;DR

This paper investigates how entanglement entropy in boosted black brane backgrounds obeys a modified first law of thermodynamics up to third order, revealing the importance of entanglement chemical potential and temperature adjustments.

Contribution

It extends the first law of entanglement thermodynamics to third order for boosted black branes, including higher order corrections and the role of entanglement chemical potential.

Findings

Third-order corrections significantly modify the first law.

Entanglement chemical potential plays a crucial role in boosted backgrounds.

Modified entanglement temperature and chemical potential are necessary for higher order accuracy.

Abstract

Gauge/gravity duality relates an AdS black hole with uniform boost with a boosted strongly-coupled CFT at finite temperature. We study the perturbative change in holographic entanglement entropy for strip sub-region in such gravity solutions up to third order and try to formulate a first law of entanglement thermodynamics including higher order corrections. The first law receives important contribution from an entanglement chemical potential in presence of boost. We find that suitable modifications to the entanglement temperature and entanglement chemical potential are required to account for higher order corrections. The results can be extended to non-conformal cases and AdS plane wave background.