This is why, besides some very special cases, typical statistical ensembles of quantum particles are far from being pure, and in most cases (certainly including the thermodynamic equilibrium), a good ...This is why, besides some very special cases, typical statistical ensembles of quantum particles are far from being pure, and in most cases (certainly including the thermodynamic equilibrium), a good approximation for their description is given by the opposite limit of the so-called classical mixture, in which all off-diagonal matrix elements of the density matrix equal zero, and its diagonal elements Wmm are merely the probabilities Wm of the corresponding eigenstates.