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In statistical mechanics, Maxwell-Boltzmann statistics describes the statistical distribution of material particles over various energy states in thermal equilibrium, when the temperature is high enough and density is low enough to render quantum effects negligible. Maxwell-Boltzmann statistics are therefore applicable to almost any terrestrial phenomena for which the temperature is above a few tens of kelvins.

In statistical mechanics, Bose-Einstein statistics (or more colloquially B-E statistics) determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium.

Fermi-Dirac and Bose-Einstein statistics apply when quantum effects have to be taken into account and the particles are considered "indistinguishable".

In statistical mechanics, Fermi-Dirac statistics is a particular case of particle statistics developed by Enrico Fermi and Paul Dirac that determines the statistical distribution of fermions over the energy states for a system in thermal equilibrium. In other words, it is a probability of a given energy level to be occupied by a fermion. Fermions are particles which are indistinguishable and obey the Pauli exclusion principle, i.e., no more than one particle may occupy the same quantum state at the same time.

In quantum mechanics and statistical mechanics, parastatistics is one of several alternatives to the better known particle statistics models (Bose-Einstein statistics, Fermi-Dirac statistics and Maxwell-Boltzmann statistics). Other alternatives include anyonic statistics and braid statistics, both of these involving lower spacetime dimensions.