Simple Quantitative Tests to Validate Sampling from Thermodynamic Ensembles

It is often difficult to quantitatively determine if a new molecular simulation algorithm or software properly implements sampling of the desired thermodynamic ensemble. We present some simple statistical analysis procedures to allow sensitive determination of whether the desired thermodynamic ensemble is properly sampled. These procedures use paired simulations to cancel out system dependent densities of state and directly test the extent to which the Boltzmann distribution associated with the ensemble (usually canonical, isobaric?isothermal, or grand canonical) is satisfied. We demonstrate the utility of these tests for model systems and for molecular dynamics simulations in a range of situations and describe an implementation of the tests designed for end users.