The Fefferman-Graham metric is frequently used for derivation of the first
law of the entanglement thermodynamics. On ther other hand, the entanglement
thermodynamics is well formulated by the Hessian geometry. The aim of this work
is to relate them with each other by finding the corresponding Hessian
potential. We find that the deformation of the bulk Hessian potential for the
pure AdS spacetime behaves as a source potential of the boundary Fisher metric,
and the deformation coincides with the Fefferman-Graham metric. A peculiar
feature different from related works is that we need not to use the
Ryu-Takayanagi formula for the above derivation. The canonical parameter space
in the Hessian geometry is a kind of the model parameter space, rather than the
real classical spacetime in the usual setup of the AdS/CFT correspondence.
However, the underlying mathematical structure is the same as that of the
AdS/CFT correspondence. This suggests the presence of more global class of
holographic transformation.