Fundamental forces and Pauli's exclusion principle

The Pauli exclusion principle exists independently of the fundamental forces. It exists also among non-interacting particles of the same kind (if such actually existed).

 

I asked a similar question a while ago, and there were a few pages of discussion that you may like to read through: https://www.physicsforums.com/showthread.php?t=409034

That thread also contains links to other threads and websites.

 

Has anyone formulated thay the PEP as an entropic force, or proven that it can't be?

 

The exclusion principle and it's resulting "something-which-looks-like-a-force" are unrelated to entropy. These are two completely different concepts. Entropy is not even a property of a micro system (i.e., a system in a pure state)!