Is there an expression similar to the Sackur-Tetrode equation that describes the statistical entropy of fermions or bosons, maybe for the electron gas in a metal or the photon gas in a cavity?
There are expressions for the entropy (or heat capacity) of ideal Fermi or Bose gases derived from quantum statistical physics (see, for example: [PDF]Statistical Physics - ETH Zürich).
Now I've looked at Feder's lecture notes. I've appended a text of my own where in the expression for ln W in sections 1 and 3 I get the same as equation 4.6 in Feder, apart from a minus in front of one of the terms. Don't know where the mistake is.
Anyway: I'd like to know if it's possible to simplify this expression as sketched in the text. My problem is that I'm left with 1 term I can't simplify at the end of section 3. Do you know if this is done anywhere?
Compare your expression for lnW to equation (5.9) in “Statistical Mechanics” by J. E. Mayer and M. G. Mayer (https://archive.org/details/statisticalmecha029112mbp). It seems to me that David L. Feder made a sign error in his course notes.