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We propose a sequence of steps and a generic transformation for connectingcommon thermodynamic quantities considered in asymptotically anti-de Sitterblack hole thermodynamics in the bulk and those that are appropriate for CFTthermodynamics in the boundary. We do this by constructing a "varying-$G$ map",where $G$ is the gravitational constant, and demonstrate its usefulness byconsidering various examples.

A varying gravitational constant map in asymptotically AdS black hole thermodynamics