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A possible quantum-mechanical origin of statistical mechanics is discussed,and microcanonical and canonical ensembles of bosons and fermions are derivedfrom the stationary Schr\"odinger equation in a unified manner. The interactionHamiltonians are constructed by the use of the discrete phase operators and thegauge-theoretical structure associated with them. It is shown how theinteraction Hamiltonians stipulated by the gauge symmetry generate the specificpatterns of entanglement that are desired for establishing microcanonicalensembles. A discussion is also made about the interrelation between randomphases and perfect decoherence in the vanishing-interaction limit.

Derivation of Bose-Einstein and Fermi-Dirac statistics from quantum mechanics: gauge-theoretical structure