Entanglement entropy and subregion complexity in thermal perturbations around pure AdS spacetime

Abstract

We compute the holographic entanglement entropy and subregion complexity of spherical boundary subregions in the uncharged and charged anti-de Sitter (AdS) black hole backgrounds, with the change in these quantities being defined with respect to the pure AdS result. This calculation is done perturbatively in the parameter R z h , where z h is the black hole horizon and R is the radius of the entangling region. We provide analytic formulas for these quantities as functions of the boundary spacetime dimension d including several orders higher than previously computed. We observe that the change in entanglement entropy has a definite sign at each order and subregion complexity has a negative sign relative to entanglement entropy at each of those orders (except at first order or in three spacetime dimensions, at which it vanishes identically). We combine preexisting work on the "complexity equals volume" conjecture and the conjectured relationship between Fisher information and bulk entanglement to suggest a refinement of the so-called first law of entanglement thermodynamics by introducing a work term associated with complexity. This extends the previously proposed first law, which held to first order, to one that holds to second order. We note that the proposed relation does not hold to third order and speculate on the existence of additional informationtheoretic quantities that may also play a role.

Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

“…Finally, to conclude, we would like to mention that ideas of complexity in the field theory side are still developed partially [89][90][91][92][93][94][95][96][97]. 9 Hence, we followed the gravitational (holographic) mixed state complexity proposal previously explored in various literature [72,80,[98][99][100][101][102][103][104] and applied in the model studied in this paper. The results indicate a universality in the jump of radiation complexity at Page time and provide us with some hope that the path being followed is somewhat self-consistent.…”

Purification complexity without purifications

“…As extensions of these conjectures for pure states to mixed states, the gravitational dual of the mixed-state complexity associated with reduced density operators for subregions on the boundary of asymptotically AdS spaces are proposed to be subregion vol-ume=complexity (sub-CV) [79,80] and subregion action=complexity (sub-CA) [80]. For more studies on that direction, see e.g., [36,37,[81][82][83][84][85][86] and references therein. Based on these proposals for subregion complexity, [82] has studied the additivity properties and examined whether they are holographic purification complexity, i.e., the minimum holo-…”

Universal pieces of holographic entanglement entropy and holographic subregion complexity

“…As discussed in the Introduction, one motivation for the modified definition (2.2) is that the universal piece ofC A is proportional to that of S A whereas a direct application of (1.5) does not guarantee that (see Appendix). Such a simple relation between S A and C A is implicit in [10] and has been further explored in [27][28][29] where AdS spacetimes are considered without any explicit embeddings in string or M theory. We revisit those calculations both for HEE and HSC now in the context of the generic metric with warped AdS factor given in (2.1) to prove the proportionality claim.…”