Equilibrium free energy estimates based on nonequilibrium work relations and extended dynamics

Area of Science:

• Statistical mechanics
• Thermodynamics
• Computational physics

Background:

• Jarzynski's relation and fluctuation theorem link nonequilibrium statistical mechanics to equilibrium thermodynamics.
• The relationship between equilibrium free energy and nonequilibrium work is valuable for computational simulations.
• Free energy is a state function, invariant to the pathway of ensemble change.

Purpose of the Study:

• To present a generalized expression for free energy differences.
• To propose several novel computational methods based on this generalized expression.
• To evaluate the accuracy and efficiency of these proposed methods.

Main Methods:

• Exploiting the state function property of free energy.
• Developing a generalized expression for free energy differences.
• Applying proposed methods to a model problem for evaluation.

Main Results:

• A generalized expression was found to be advantageous for free energy difference simulations.
• Several new computational methods were proposed.
• The accuracy and efficiency of the proposed methods were assessed on a model system.

Conclusions:

• The proposed generalized expression and associated methods offer an effective approach for computing free energy differences in simulations.
• This work advances the application of nonequilibrium statistical mechanics in computational thermodynamics.
• The findings are relevant for molecular simulations and computational studies of thermodynamic systems.