  A novel error measure, referred to as the hysteresis error, is developed from
the Crooks fluctuation theorem to evaluate sampling quality in free energy
calculations. Theory and numerical free energy of hydration calculations are
used to show that Hamiltonian replica exchange provides a direct route for
minimizing the hysteresis error. Replica exchange swap probabilies yield the
rate at which the hysteresis error falls with simulation length, and this
result can be used to decrease bias and statistical errors associated with free
energy calculations based on multicanonical simulations.
