Satisfying the fluctuation theorem in free energy calculations with Hamiltonian replica exchange

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.