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We examine the validity of nonlinear thermodynamic models which incorporate the contribution of electrostatic coupling and interfacial space charge in ferroelectric-paraelectric bilayers.Inconsistency of the directions between build-in polarization and field is found.Evolution of ferroelectricity does not follow the variation in coupling strength between different layers.In addition,we observe that the field-induced polarization in the paraelectric layer deviates from the polarization derived by thermodynamic theory.These findings indicate that the current versions of thermodynamic models need to be modified.