When the system has a large number of degrees of freedom, an analytical expression for ⟨ ⟨ Q ⟩ ⟩ is often hard to obtain, and Monte Carlo integration is typically employed in the computation of ⟨ ⟨ Q ⟩ ⟩ . On the simplest formulation, the method chooses N uniformly distributed states r i ∈ ∈ Ω Ω , and uses the estimator