Abstract: In order to apply quantum statistical mechanics to systems composed of Josephson junctions, the unconventional constraint of fixed “macroscopic wave function” magnitudes on either side of a junction must be accommodated. In order to use this information, the density matrix formalism must be extended to deal directly with probability distributions over general quantum states. As a result, in thermal equilibrium, the explicit temperature dependence becomes modified from the trivial 1/kT factors.