# What is the range of degeneracy pressure?

In what way is degeneracy pressure related to the separation of fermions? Is there any influence at ranges like a meter and beyond. I expect the influence at those ranges to be immeasurably small. I just wonder if theory predicts an effect or if there is truly zero degeneracy pressure at long range.

I'm under the impression that if you have a block of iron that is a solid cubic meter, then each and every electron in that block will be found in a slightly different quantum state at any given moment. This being due to the PEP.

• Hi Alex, I saw your question above and it prompted me to ask a related one, I had always assumed degeneracy pressure did not apply in normal situations, physics.stackexchange.com/questions/197742/… – user81619 Aug 4 '15 at 23:27
• Hey, hopefully we both get an answer. – Alex Aug 4 '15 at 23:46
• I got this quote as a comment and it might apply to your question "At commonly encountered densities, this pressure is so low that it can be neglected." I would guess because it's not an electro-magnetic effect (afaik), but instead the PEP, it may have finite range and is zero at finite range, just a guess, best of luck with an answer from some who really knows. Also, if the PEP only applies within atoms, to prevent overfilling of energy levels, would that be affected by an atom relatively far away...bit out of my depth – user81619 Aug 5 '15 at 0:32
• I'm under the impression that if you have a block of iron that is a solid cubic meter, then each and every electron in that block will be found in a slightly different quantum state at any given moment. This being due to the PEP. – Alex Aug 5 '15 at 0:42
• Put that above comment in your post, definitely. It clarifies your question a lot. If I have you right, you are saying the PEP may still "push" the neighbouring atoms outer electrons a little bit from their normal orbital position? – user81619 Aug 5 '15 at 1:01

If the fermions are non-relativistic, the degeneracy pressure scales as $n^{5/3}$, where $n$ is the fermion number density. Thus for a fixed number of fermions the pressure decreases more rapidly than the volume increases.