<p>Kelvin’s curvature theory (the Kelvin paradigm) has been traditionally accepted as a fundamental concept in surface thermodynamics, yet its dependence on curvature limits its applicability to surface effect evaluation of chemical potentials of nano-objects with surfaces possessing well-defined curvatures. This paper demonstrates and confirms a Gibbsian thermodynamic approach or paradigm as an alternative to the Kelvin theory, capable of quantifying the surface-induced chemical potential of any nano-object based on its differential surface-to-volume ratio without relying on surface curvature. Consequently, this Gibbsian paradigm not only can duplicate the predictions of the established Kelvin theory, it may also&#xa0;be applied beyond the curvature-constraint of the Kelvin theory, thereby providing&#xa0; a general method to correctly analyze and characterize surface effects on nano-objects across all common external geometric configurations. In evaluation of nano-objects with fully defined principal surface curvatures, both the Kelvin and the Gibbsian paradigms align and predict the same surface effect. For nano-objects with partially defined curvatures such as a cylindrical nano-wire, the Kelvin paradigm always underestimates the surface effect. For nano-objects with no defined curvature, e.g., a planar thin film, the Kelvin paradigm unrealistically predicts no surface effect, while the Gibbsian paradigm properly provides a significant one. Contrary to the Kelvin paradigm, the Gibbsian paradigm also convincingly demonstrates that a nano-object even with extremely low principal surface curvatures would have a relatively higher chemical potential, and thereby a lower thermodynamic stability compared to its spherical counterpart of the same composition and volume.</p>