  Black holes exert quantum pressure coming from the nonlocal gravity
correction. We investigate this nonlocal correction for black holes in anti-de
Sitter (AdS) spacetime and its dual boundary field theory. We show that the
second order curvature and the nonlocal actions do not backreact on the AdS
black hole metric. Thus, the interpretation of quantum pressure holds in the
bulk for AdS black hole, generalizing the previous result for the
asymptotically flat black hole. We then show that the leading geometric
correction comes from the third order in curvature and explicitly calculate the
corrections to the metric and to the horizon. For applications to AdS/CFT, we
conjectured a nonlocal Gibbons-Hawking-York boundary term along with the
necessary counter terms to cancel the ultraviolet divergence of the bulk
action. We then calculate the thermodynamic quantities in the bulk and discuss
their properties.
