So I was looking over some of the formalism of the density matrix in Kurt Gottfried & Tung-Mow Yan's Quantum Mechanics: Fundamentals. For atoms in thermal equilibrium, they give the mixed state probability that the system is in a certain energy eigenstate using the boltzmann distribution. Why is this valid? Should they not be using the bose-einstein or fermi-diract distribution for bosons/fermions respectively. I think I understand that the mixed state probabilities are thought of as a classical uncertainty on the state of the system, however, It still seems like if the system is composed of indistinguishable particles, they'd have to give the appropriate distribution function for such a case.