# Van der Waals-like Behaviour of Charged Black Holes and Hysteresis in the Dual QFTs

## TL;DR

This paper investigates the temperature-dependent hysteresis in the shear viscosity to entropy density ratio of dual QFTs, linking it to the Van der Waals-like thermodynamics of charged black holes in AdS space.

## Contribution

It introduces a spherical analogue of shear viscosity in holography and explains hysteresis phenomena via black hole thermodynamics and phase transitions.

## Key findings

- Hysteresis in /s observed in charged black holes.
- Hysteretic behavior linked to Van der Waals-like phase transitions.
- System evolution depends on path through meta-stable states.

## Abstract

Using the rules of the AdS/CFT correspondence, we compute the spherical analogue of the shear viscosity, defined in terms of the retarded Green function for the stress-energy tensor for QFTs dual to five-dimensional charged black holes of general relativity with a negative cosmological constant. We show that the ratio between this quantity and the entropy density, $\tilde\eta/s$, exhibits a temperature-dependent hysteresis. We argue that this hysteretic behaviour can be explained by the Van der Waals-like character of charged black holes, considered as thermodynamical systems. Under the critical charge, hysteresis emerges owing to the presence of two stable states (small and large black holes) connected by a meta-stable region (intermediate black holes). A potential barrier prevents the equilibrium path between the two stable states; the system evolution must occur through the meta-stable region, and a path-dependence of $\tilde\eta/s$ is generated.