On thermodynamic observables and the Anderson model

A thermodynamic observable is approximately additive under the decomposition of the volume. This property is of particular relevance to disordered systems. If scaled by the size of the system (N) a thermodynamic observable converges with probability one to a non-random limit as N to infinity inasmuch as one may apply the ergodic theorem. The author presents a simple argument to prove that the density of states in the Anderson model is a thermodynamic observable. Both diagonal and off-diagonal disorder are discussed, and the relation to the replica method is indicated.