Abstract
This paper studies the thermodynamic geometry of the Reissner-Nordström-anti-de Sitter(RN-AdS)black hole via detection of the non-local observables in the dual field theory,including the entanglement entropy and equal-time two-point correlation function.With the dimensional analysis,we construct the principle of corresponding states of black hole thermodynamics.As a result,our findings can be applied to black holes with different AdS backgrounds.In this sense,the probe of the thermodynamic geometry of the RN-AdS black hole though the non-local observables in dual field theory has been confirmed numerically.
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