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For a gas of self-interacting electrons (i.e. a non-ideal Fermi gas), is there is there any sense in trying to define an equation of state? If so, what is the equation of state for a gas of electrons? That is, can one define a thermodynamic pressure $P$ as a function of the electron density $\eta$ and temperature $T$?

Any direction would help immensely.

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    $\begingroup$ You basically need to follow the derivation for the equation of state in the ideal case (get the partition function, derive thermodynamic equations from it), using a Hamiltonian H which includes the interaction term. Depending on the interaction, this may not be analytically tractable. $\endgroup$ – AGML Oct 4 '16 at 21:20
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    $\begingroup$ Well, it'll be done for the ideal case in basically any stat mech textbook. For gasses with interactions I'm less sure; you might need to do some kind of perturbation theory depending on the interaction. This will be discussed also in most stat mech books or, failing that, books on quantum many-body theory. $\endgroup$ – AGML Oct 4 '16 at 21:45
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    $\begingroup$ Also, check out this paper where they give a pressure equation for a Fermi superfluid. Maybe the references in that paper can guide you further. $\endgroup$ – tpg2114 Oct 4 '16 at 21:57
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    $\begingroup$ There's a lot of experimental and theoretical work on this in the last few years in the context of strongly-interacting ultracold fermions. For example, start here: science.sciencemag.org/content/328/5979/729 $\endgroup$ – Rococo Oct 4 '16 at 22:15
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    $\begingroup$ If you Google "[PDF]Chapter 13 Ideal Fermi gas" you will be able to download the file, all_1314_chap13-2.pdf. which is a derivation of the ideal gas law as a starting point, then perhaps follow the comments and procedure outlined by AGML to obtain the non ideal gas law $\endgroup$ – user108787 Oct 4 '16 at 22:33

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