We study the extended thermodynamics, obtained by considering the cosmological constant as a thermodynamic variable, of STU black holes in 4-dimensions in the fixed charge ensemble. The associated phase structure is conjectured to be dual to an RG-flow on the space of field theories. We find that for some charge configurations the phase structure resembles that of a Van der Waals gas: the system exhibits a family of first order phase transitions ending in a second order phase transition at a critical temperature. We calculate the holographic entanglement entropy for several charge configurations and show that for the cases where the gravity background exhibits Van der Waals behavior, the entanglement entropy presents a transition at the same critical temperature. To further characterize the phase transition we calculate appropriate critical exponents and show that they coincide. Thus, the entanglement entropy successfully captures the information of the extended phase structure. Finally, we discuss the physical interpretation of the extended space in terms of the boundary QFT and construct various holographic heat engines dual to STU black holes.

We study the complexity of Gaussian mixed states in a free scalar field theory using the ‘purification complexity’. The latter is defined as the lowest value of the circuit complexity, optimized over all possible purifications of a given mixed state. We argue that the optimal purifications only contain the essential number of ancillary degrees of freedom necessary in order to purify the mixed state. We also introduce the concept of ‘mode-by- mode purifications’ where each mode in the mixed state is purified separately and examine the extent to which such purifications are optimal. We explore the purification complexity for thermal states of a free scalar QFT in any number of dimensions, and for subregions of the vacuum state in two dimensions. We compare our results to those found using the various holographic proposals for the complexity of subregions. We find a number of qualitative similarities between the two in terms of the structure of divergences and the presence of a volume law. We also examine the ‘mutual complexity’ in the various cases studied in this paper.

We use the notion of double holography to study Hawking radiation emitted by the eternal BTZ black hole in equilibrium with a thermal bath, but in the form of warped CFT₂ degrees of freedom. In agreement with the literature, we find entanglement islands and a phase transition in the entanglement surface, but our results differ significantly from work in AdS/CFT in three major ways: (1) the late-time entropy decreases in time, (2) island degrees of freedom exist at all times, not just at late times, with the phase transition changing whether or not these degrees of freedom include the black hole interior, and (3) the physics involves a field-theoretic IR divergence emerging when the boundary interval is too big relative to the black hole’s inverse temperature. This behavior in the entropy appears to be consistent with the non-unitarity of holographic warped CFT₂ and demonstrates that the islands are not a phenomenon restricted to black hole information in unitary setups.

We study the effect of a non-vanishing chemical potential on the thermalization time of a strongly coupled large Nc gauge theory in (2 + 1)-dimensions, using a specific bottom-up gravity model in asymptotically AdS space. We first construct a perturbative solution to the gravity-equations, which dynamically interpolates between two AdS black hole backgrounds with different temperatures and chemical potentials, in a perturbative expansion of a bulk neutral scalar field. In the dual field theory, this corresponds to a quench dynamics by a marginal operator, where the corresponding coupling serves as the small parameter in which the perturbation is carried out. The evolution of non-local observables, such as the entanglement entropy, suggests that thermalization time decreases with increasing chemical potential. We also comment on the validity of our perturbative analysis.

We study the black hole information problem within a semiclassically gravitating AdS _d d black hole coupled to and in equilibrium with a d d -dimensional thermal conformal bath. We deform the bath state by a relevant scalar deformation, triggering a holographic RG flow whose "trans-IR" region deforms from a Schwarzschild geometry to a Kasner universe. The setup manifests two independent scales which control both the extent of coarse-graining and the entanglement dynamics when counting Hawking degrees of freedom in the bath. In tuning either, we find nontrivial changes to the Page time and Page curve. We consequently view the Page curve as a probe of the holographic RG flow, with a higher Page time manifesting as a result of increased coarse-graining of the bath degrees of freedom.