Subtle energy difference determining the delicately stable state of a solid object on a liquid medium with an arbitrary surface area

Highlights: • From the potential energy concept, we confirmed that the Archimedes' principle is perfectly applicable for a liquid medium with an arbitrary surface area being either limited or infinitely large. • We quantitatively conceptualized a pseudopotential field of buoyancy. • After accounting the pseudopotential energy of buoyancy into the total potential energy of a floating object, we proved the general physical criterion: a delicately stable state is the practical state with the lowest total potential energy which cannot tolerate a subtly higher potential energy. -- Abstract: Even though it was put forth 2200 years ago, Archimedes' principle of buoyancy still has secrets. From the potential energy concept, we confirm that this principle is perfectly applicable for a liquid medium with an arbitrary surface area being either limited or infinitely large. After we quantitatively conceptualize the pseudopotential field of buoyancy, account the pseudopotential energy of buoyancy as part of the total potential energy of a floating object, and immerse uniform cubic toy blocks with various densities in different immersing types into a tank of water with a limited surface, we prove the following general physical criterion: a delicately stable state is the state with the lowest total potential energy which cannot tolerate a subtly higher potential energy. The pseudopotential energy of buoyancy has a significant possibility of being used in obtaining the expected delicate immersion stability of a manmade object on a liquid surface and of being popularized in related hydraulic systems.