Fermi-Dirac statistics is a type of quantum statistics that applies to the physics of a system consisting of many identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each of whom derived the distribution independently in 1926 (although Fermi derived it before Dirac). Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics.
Fermi–Dirac (F–D) statistics applies to identical and indistinguishable particles with half-integer spin (1/2, 3/2, etc.), called fermions, in thermodynamic equilibrium. For the case of negligible interaction between particles, the system can be described in terms of single-particle energy states. A result is the F–D distribution of particles over these states where no two particles can occupy the same state, which has a considerable effect on the properties of the system. F–D statistics is most commonly applied to electrons, a type of fermion with spin 1/2.
A counterpart to F–D statistics is Bose–Einstein (B–E) statistics, which applies to identical and indistinguishable particles with integer spin (0, 1, 2, etc.) called bosons. In classical physics, Maxwell–Boltzmann (M–B) statistics is used to describe particles that are identical and treated as distinguishable. For both B–E and M–B statistics, more than one particle can occupy the same state, unlike F–D statistics.