(possible distribution of particles bound by Pauli exclusion)
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, gluons,
and some baryons.
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.