Recently, remarkable progress in recovering the Page curve of an evaporating black hole (BH) in Jackiw-Teitelboim gravity has been achieved through use of Quantum Extremal surfaces (QES). Multi-boundary Wormhole (MbW) models have been crucial in parallel model building in three dimensions. Motivated by this we here use the latter models to compute the subregion complexity of the Hawking quanta of the evaporating BH in AdS3 and obtain the Page curve associated with this information theoretic measure. We use three- and n-boundary wormhole constructions to elucidate our computations of volumes below the Hubeny-Rangamani-Takayanagi (HRT) surfaces at different times. Time is represented by the growing length of the throat horizons corresponding to smaller exits of the multi-boundary wormhole and the evaporating bigger exit shrinks with evolving time. We track the change in choice of HRT surfaces with time and plot the volume with time. The smooth transition of Page curve is realized by a discontinuous jump at Page time in volume subregion complexity plots and the usual Page transition is realized as a phase transition due to the inclusion of the island in this context. We discuss mathematical intricacies and physical insights regarding the inclusion of the extra volume at Page time. The analysis is backed by calculations and lessons from kinematic space and tensor networks.

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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.