The potential energy differences ∆u ij are evaluated for samples taken from a single simulation and assess the work which would be required to move the system from one state (or one Hamiltonian) to the other. A simulation in state i can be said to have coordinates x i , and from that simulation we evaluate ∆u ij (x i ), the energy difference to alter the energy function to that corresponding to state j. Likewise, we also use snapshots from the simulation run in state j to compute ∆u ij (x j ). Here, ∆u ij (x) = u j (x) -u i (x). In this notation, the potential energy u i (x) refers to a dimensionless reduced potential function that includes the pressure-volume work; this allows easier accommodation of the equations to different choices of ensemble; here, calculations are performed in the isothermalisobaric ensemble: