Holographic Entanglement Entropy and Van der Waals transitions in Einstein-Maxwell-dilaton theory

TL;DR

This paper investigates Van der Waals phase transitions in charged dilatonic AdS black holes within Einstein-Maxwell-dilaton theory, revealing a special class exhibiting standard Van der Waals behavior and corresponding holographic entanglement entropy transitions.

Contribution

The study identifies a unique class of charged dilatonic AdS black holes with standard Van der Waals transitions and analyzes their thermodynamics and holographic entanglement entropy behavior.

Findings

Black holes show standard Van der Waals transitions in thermodynamics.

Holographic entanglement entropy exhibits the same transition behavior.

Near-horizon geometry is conformal to AdS2 x S^{D-2} in extremal limit.

Abstract

According to the gauge/gravity duality, the Van der Waals transition of charged AdS black holes in extended phase space is conjectured to be dual to a renormalization group flow on the space of field theories. So exploring the Van der Waals transition is potentially valuable for studying holographic properties of charged black hole thermodynamics. There are different transition behaviors for charged dilatonic AdS black holes in Einstein-Maxwell-dilaton (EMD) theory with string-inspired potential with different dilaton coupling constants in diverse dimensions. In this work, we find a special class of charged dilatonic AdS black holes which have the standard Van der Waals transition. We study the extended thermodynamics of the special class of black holes, which, in the extremal limit, have near-horizon geometry conformal to AdS$_2 \times S^{D-2}$. We find that, for these black holes, both the pressure-volume transition in fixed charge ensemble and the inverse temperature-entropy transition in fixed pressure ensemble have the standard Van der Waals behaviors. We also find the holographic entanglement entropy undergoes the same transition behaviors for the same critical temperature in fixing the thermodynamic pressure ensemble.