Fermi-Dirac Statistics

Fermi-Dirac statistics is a set of rules in quantum statistical mechanics describing how a large number of identical particles that obey the Pauli exclusion principle, known as fermions, distribute themselves among available energy states at thermal equilibrium. Italian physicist Enrico Fermi and English physicist Paul Dirac independently developed the statistics in 1926, building on Wolfgang Pauli's 1925 exclusion principle, which holds that no two identical fermions can occupy the same quantum state simultaneously. Because of this exclusion, the statistics differ sharply from classical statistics: at low temperature, fermions fill up the lowest available energy states one at a time up to a maximum level called the Fermi energy, rather than clustering in the single lowest state as bosons do under Bose-Einstein statistics. Fermi-Dirac statistics apply to particles such as electrons, protons and neutrons, and are essential to explaining the electrical behavior of metals and semiconductors and the structure of white dwarf and neutron stars, where electron or neutron degeneracy pressure counteracts gravitational collapse.