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Fermi-Dirac statistics (F-D statistics or the Fermi-Dirac distribution) describes a distribution of the energy levels of non-interacting, distinguishable particles if they are in thermodynamic equilibrium and are fermions, i.e., bound by the Pauli exclusion principle. The Pauli exclusion principle is the fact that no more than one such particle within a quantum system will ever occupy the same quantum state. The analogous distribution of the energy-levels of particles not so-bound (which are termed bosons) is called Bose-Einstein statistics (B-E statistics or the Bose-Einstein Dirac distribution).
Fermions include quarks, protons, and neutrons, whereas bosons include photons and gluons. If the temperature is sufficiently high and/or the particles are at a sufficiently low concentration, both Fermi-Dirac statistics and Bose-Einstein statistics approach the classical formulation, Maxwell-Boltzmann statistics.