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What is the origin of the name "degeneracy" pressure and "degenerate" Fermi gas? I was trying to find the first paper that used the term "degenerate/degeneracy" to describe either "degeneracy" pressure or "degenerate" Fermi gas. But I failed to do so. Any help is highly appreciated!

Edit: I want to know if there is a reason why people call it degeneracy here. As an example, the "canonical" in the canonical quantization and canonical ensemble are two distinct physics meanings at first glance. But if we think more carefully, both are the adjectives that mean "the standard way". So, I was wondering if something is "degenerate" in this context. Is that because they are approaching a single multi-particle ground state with zero entropy?

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    $\begingroup$ This contains some leads: Degenerate matter. Note that the question is really not about physics - more history of science. $\endgroup$ Sep 23 at 8:42
  • $\begingroup$ Search term: moral turpitude $\endgroup$
    – rob
    Sep 23 at 15:35

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The term "degeneracy" comes from mathematics, where it refers to special "edge cases" in the math. The degenerate Fermi gas is an edge case (zero temperature) of a gas composed of fermions.

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  • $\begingroup$ Indeed, agreed. The sense Fermi used it in 1926 was "limiting case", as well. $\endgroup$ Sep 23 at 20:29
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In this discussion of degeneracy pressure there is also a remark about the origin of the name:

Of course, de­gen­er­acy pres­sure is a poorly cho­sen name. It is re­ally due to the fact that the en­ergy dis­tri­b­u­tion of elec­trons is not de­gen­er­ate, un­like that of bosons.



A population of bosons can all be in the same quantum state, allowing the population as a whole to have very little energy content.

For a population of electrons (fermions), the lowest available energy state is still one where no two fermions occupy the same quantum state.

When a solid is forcefully compressed less space is available for the electrons of the atoms that the solid consists of. In that compressed state the orbital motion of the electrons has a larger kinetic energy than in uncompressed state. That is, the work done in compressing a solid goes to kinetic energy of the electrons.

The highest pressure state possible for matter consisting of nuclei with electrons around them is in the interior of a star on the verge of collapsing to a neutron star.

A state of being a neutron star is a much higher energy state than a state of nuclei with electrons around them.

In the final collapse to a state of being a neutron star the pressure from gravity is finally sufficiently large such that the gravitational potential energy released in the contraction is enough for the transition to neutron star state to occur.

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  • $\begingroup$ I agree that the name "de­gen­er­acy" in this context is poorly chosen. But I just get confused about if there is a reason why people call it degeneracy here. As an example, the "canonical" in the canonical quantization and canonical ensemble are two distinct physics meanings at first glance. But if we think more carefully, both are the adjectives that mean "the standard way". So, I was wondering if something is "degenerate" in this context. Is that because they are approaching a single multi-particle ground state with zero entropy? $\endgroup$
    – Cory
    Sep 23 at 15:03

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