The Hamitonian, H(λ, x), is dependent on λ and on the positions and momenta of all particles in the system, x, but is written H for brevity. The free energy change calculated is only an estimate (denoted by the hat operator) because we cannot fully enumerate the desired ensemble. Instead, ⟨...⟩ λ denotes an average obtained from statistical sampling (molecular dynamics) at λ and taken to be equivalent to the ensemble average (the ergodic hypothesis).