Degenerate matter in physics is a collection of free, non-interacting particles with a pressure and other physical characteristics determined by quantum mechanical effects. It is the counterpart of an ideal gas in classical mechanics. The degenerate state of matter (in the sense of deviant from an ideal gas) arises at extraordinarily high density (in compact stars) or at extremely low temperatures (in the lab). It occurs for matter particles such as electrons, neutrons and protons, in general fermions and is referred to as electron-degenerate matter, neutron-degenerate matter, etc. In a mixture of particles, such as ions and electrons in white dwarfs, the electrons may be degenerate, while the ions are not.

In a quantum mechanical description, free particles limited to a finite volume may only take a discrete set of energies, called quantum states. The Pauli Exclusion Principle prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. The pressure (called degeneracy pressure or Fermi-pressure) remains finite even near absolute zero temperature. Adding particles or reducing the volume forces the particles into higher-energy quantum states. This requires a compression force, and is made manifest as a resisting pressure. The key feature is that this degenerate pressure does not depend on the temperature and only on the density of the fermions. It keeps dense stars in equilibrium independent of the thermal structure of the star.