quantum mechanics - How can Pauli's exclusion principle originate forces?

Recently I've seem two situation in which the Pauli exclusion principle is said to originate forces.

The first was a derivation of the Lennard-Jones potential in the context of Solid State Physics aimed to explain the molecular binding. The second is the exchange interaction in ferromagnetism.

The idea seems to be in the general case that the Pauli exclusion principle is the reason why some repulsive interactions appear.

Now, what I know is that the principle states that a system of fermions can't have two fermions with the same quantum numbers.

How can a qualitative principle like that originate one interaction? And furthermore, how can one derive a potential for such interaction? Because in either cases I cited, a potential is derived (the Lennard-Jones potential and the exchange interaction potential energy).