Editing Degenerate matter (section)

== Degeneracy pressure ==
Unlike a classical [[ideal gas]], whose pressure is proportional to its [[temperature]]
<math display="block">P=k_{\rm B}\frac{NT}{V}, </math>
where ''P'' is pressure, ''k''<sub>B</sub> is the [[Boltzmann constant]], ''N'' is the number of particles (typically atoms or molecules), ''T'' is temperature, and  ''V'' is the volume, the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at [[absolute zero]] temperature. At relatively low densities, the pressure of a fully degenerate gas can be derived by treating the system as an ideal Fermi gas, in this way
<math display="block">P=\frac{(3\pi^2)^{2/3}\hbar^2}{5m} \left(\frac{N}{V}\right)^{5/3},</math>
where ''m'' is the mass of the individual particles making up the gas. At very high densities, where most of the particles are forced into quantum states with [[Kinetic energy#Relativistic kinetic energy of rigid bodies|relativistic energies]], the pressure is given by
<math display="block">P=K\left(\frac{N}{V}\right)^{4/3},</math>
where ''K'' is another proportionality constant depending on the properties of the particles making up the gas.<ref>''Stellar Structure and Evolution'' section 15.3 – R Kippenhahn & A. Weigert, 1990, 3rd printing 1994. {{ISBN|0-387-58013-1}}</ref>

[[File:Quantum ideal gas pressure 3d.svg|thumb|Pressure vs temperature curves of a [[Ideal gas law|classical ideal gas]] and quantum ideal gases ([[Fermi gas]], [[Bose gas]]), for a given particle density.]]

All matter experiences both normal thermal pressure and degeneracy pressure, but in commonly encountered gases, thermal pressure dominates so much that degeneracy pressure can be ignored. Likewise, degenerate matter still has normal thermal pressure; the degeneracy pressure dominates to the point that temperature has a negligible effect on the total pressure. The adjacent figure shows the thermal pressure (red line) and total pressure (blue line) in a Fermi gas, with the difference between the two being the degeneracy pressure.  As the temperature falls, the density and the degeneracy pressure increase, until the degeneracy pressure contributes most of the total pressure.

While degeneracy pressure usually dominates at extremely high densities, it is the ratio between degenerate pressure and thermal pressure which determines degeneracy.  Given a sufficiently drastic increase in temperature (such as during a red giant star's [[helium flash]]), matter can become non-degenerate without reducing its density.

Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter because a significant contribution to their pressure is provided by electrical repulsion of [[atomic nucleus|atomic nuclei]] and the screening of nuclei from each other by electrons.  The [[free electron model]] of metals derives their physical properties by considering the [[Conductor (material)|conduction]] electrons alone as a degenerate gas, while the majority of the electrons are regarded as occupying bound quantum states. This solid state contrasts with degenerate matter that forms the body of a white dwarf, where most of the electrons would be treated as occupying free particle momentum states.

Exotic examples of degenerate matter include neutron degenerate matter, [[strange matter]], [[metallic hydrogen]] and white dwarf matter.