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Quantum statistical mechanics

Statistical mechanics is the description of a gas of (usually indistinguishable) particles. In cases where the temperature is low enough or the concentration is high enough then the quantum mechanical symmetry properties of the particles become important. Particles with integral spin (bosons) obey Bose-Einstein statistics and particles with half-integral spin (fermions) obey Fermi-Dirac statistics. Said another way, whether the particles' wave functions are symmetric or anti-symmetric under particle interchange determines which quantum statistics are applicable.

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