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In this paper, we show the relation between the thermodynamic geometry of afour-dimensional Reissner-Nordstrom-AdS (RN-AdS) black hole and non-localobservables in boundary field theory. Instead of introducing the critical pointassociating with the black hole charge to nondimensionalize the thermodynamicsparameters, we use the cosmological constant to rescale these variables, sothat a universal specific equation of state of the black hole is obtained.Further, the correspondence between thermodynamic properties of the black holeand the oscillating behaviors of the non-local observables has been studiednumerically. Our results indicate that the study of the dual field theory willreveal to us the thermodynamic geometry of the AdS black hole.

Thermodynamic geometry of the RN-AdS black hole and non-local observables