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## Main Question or Discussion Point

Continue reading...Commonly there is a lot of imprecision in talking about ”indistinguishable” (or ”identical”) particles, even in serious work. This Insight article clarifies the issues involved in a conceptually precise way.

Classical mechanics.Historically, indistinguishable particles were introduced in order to explain the failure of the thermodynamics of a Newtonian ##N##-particle system to describe the absence of an entropy increase when mixing two volumes of the same substance. This assumption, which has no logical basis in classical mechanics but appears as an ad hoc device to save the theory, drastically changes the state space of the multiparticle system, the phase space of functions of positions and momenta, to a much smaller space of symmetric functions of positions and momenta.

Nonrelativistic quantum mechanics.The first quantum manifestation of indistinguishable particles was the Pauli exclusion principle, which states that wave functions of a nonrelativistic...