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From the Wikipedia article of Helium-4 (emphasis by me).

For example, if superfluid helium-4 is kept in an open vessel, a thin film will climb up the sides of the vessel and overflow. In this state and situation, it is called a "Rollin film". This strange behavior is a result of the Clausius–Clapeyron relation and cannot be explained by the current model of classical mechanics, nor by nuclear or electrical models – it can only be understood as a quantum-mechanical phenomenon.

Clausius-Clapeyron relations are sets of relations obtained from the equal chemical potentials of co-existing phases (e.g. using the fact that the chemical potential of co-existing water vapor and liquid water in equilibrium are equal, we can find how the boiling point of water changes with pressure).

creepy

Source: Wikipedia

I thought this climbing happens because superfluid Helium wants to minimize its gravitational potential energy, and superfluidity allows it to climb up, which is not allowed classically. While climbing up, it is in an intermediate state with larger energy, which is not allowed in classical mechanics, but quantum mechanics allows it as this is like a tunneling process.

The chemical potential of the Helium inside the vessel and that outside it must be the same in equilibrium, but what Clausius-Clapeyron relation do we get from that? And why does the article says that this creepy behavior is a result of a Clausius-Clapeyron relation?

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