  In this paper, we show the relation between the thermodynamic geometry of a
four-dimensional Reissner-Nordstrom-AdS (RN-AdS) black hole and non-local
observables in boundary field theory. Instead of introducing the critical point
associating with the black hole charge to nondimensionalize the thermodynamics
parameters, we use the cosmological constant to rescale these variables, so
that a universal specific equation of state of the black hole is obtained.
Further, the correspondence between thermodynamic properties of the black hole
and the oscillating behaviors of the non-local observables has been studied
numerically. Our results indicate that the study of the dual field theory will
reveal to us the thermodynamic geometry of the AdS black hole.
