  We use functional, Fr\'echet, derivatives to quantify how thermodynamic
outputs of a molecular dynamics (MD) simulation depend on the potential used to
compute atomic interactions. Our approach quantifies the sensitivity of the
quantities of interest with respect to the input functions as opposed to its
parameters as is done in typical uncertainty quantification methods. We show
that the functional sensitivity of the average potential energy and pressure in
isothermal, isochoric MD simulations using Lennard-Jones two-body interactions
can be used to accurately predict those properties for other interatomic
potentials (with different functional forms) without re-running the
simulations. This is demonstrated under three different thermodynamic
conditions, namely a crystal at room temperature, a liquid at ambient pressure,
and a high pressure liquid. The method provides accurate predictions as long as
the change in potential can be reasonably described to first order and does not
significantly affect the region in phase space explored by the simulation. The
functional uncertainty quantification approach can be used to estimate the
uncertainties associated with constitutive models used in the simulation and to
correct predictions if a more accurate representation becomes available.
