Maxwell–Boltzmann statistics describes a dilute classical gas whose single-particle occupation factors have the displayed exponential form. It is the low-occupation classical limit of Bose--Einstein and Fermi--Dirac statistics. Integrating this factor over momentum gives the nonrelativistic Maxwell--Boltzmann number density when the particle energy is .
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Maxwell-Boltzmann statistics is a statistical framework used to describe the behavior of classical particles that are distinguishable and non-interacting. It is particularly applicable to systems of ideal gases where the particles obey classical mechanics. The statistics were developed by James Clerk Maxwell and Ludwig Boltzmann in the 19th century.
