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

TL;DR

This paper introduces the hysteresis error, a new metric based on the Crooks fluctuation theorem, to evaluate sampling quality in free energy calculations, demonstrating how Hamiltonian replica exchange can minimize this error for more accurate results.

Contribution

The paper develops the hysteresis error measure and shows how Hamiltonian replica exchange effectively reduces it, improving free energy calculation accuracy.

Findings

Hysteresis error correlates with sampling quality in free energy calculations.

Hamiltonian replica exchange minimizes hysteresis error.

Swap probabilities predict error reduction rate.

Abstract

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.