Electron degeneracy pressure

In astrophysics and condensed matter physics, electron degeneracy pressure is a quantum mechanical effect critical to understanding the stability of white dwarf stars and metal solids. It is a manifestation of the more general phenomenon of quantum degeneracy pressure.

The term "degenerate" here is not related to degenerate energy levels, but to Fermi–Dirac statistics close to the zero-temperature limit (temperatures much lower than the Fermi temperature, which for metals is about 10,000 K).

In metals and in white dwarf stars, electrons can be modeled as a gas of non-interacting electrons confined to a finite volume. Although there are strong electromagnetic forces between the negatively charged electrons, these forces are approximately balanced by the positive nuclei and so can be neglected in the simplest models. The pressure exerted by the electrons is related to their kinetic energy. The degeneracy pressure is most prominent at low temperatures: If electrons were classical particles, the movement of the electrons would cease at absolute zero and the pressure of the electron gas would vanish. However, since electrons are quantum mechanical particles that obey the Pauli exclusion principle, no two electrons can occupy the same state, and it is not possible for all the electrons to have zero kinetic energy. Instead, the confinement makes the allowed energy levels quantized, and the electrons fill them from the bottom upwards. If many electrons are confined to a small volume, on average the electrons have a large kinetic energy, and a large pressure is exerted.