  Motivated by the recent unified approach to the Smarr-like relation of AdS
planar black holes in conjunction with the quasi-local formalism on conserved
charges, we revisit the quantum statistical and thermodynamic relations of
hairy AdS planar black holes. By extending the previous results, we identify
the hairy contribution in the bulk and show that the holographic computation
can be improved so that it is consistent with the bulk computation. We argue
that the first law can be retained in its universal form while the relation
between the on-shell renormalized Euclidean action and its free energy
interpretation in gravity may be deformed to contain the hairy contribution in
hairy AdS black holes.
