A number of workarounds have been developed to stabilize time integration. For instance, bonds involving hydrogen atoms are often treated as rigid, which eliminates the highest frequency motions. Also, the repartitioning of masses from heavy atoms to bonded hydrogen atoms has long been found to stabilize the time integration and make the use of longer time steps possible. Such schemes, known as hydrogen mass repartitioning (HMR), were systematically applied to hydrogen atoms in proteins and lipids, 5 allowing stable simulations using 4 fs time steps. The statistical mechanical basis of all these schemes is well-established, as configuration space averages are independent of the masses in classical statistical mechanics.