Jarzynski matrix equality: Calculating the free-energy difference by nonequilibrium simulations with an arbitrary...

Area of Science:

• Statistical Mechanics
• Computational Chemistry
• Physical Chemistry

Background:

• The Jarzynski equality (JE) efficiently calculates free energies by relating nonequilibrium work to free-energy differences.
• Current JE applications are limited by the need for initial equilibrium states, restricting its use in complex systems.

Purpose of the Study:

• To extend the Jarzynski equality (JE) method to overcome the equilibrium initial state requirement.
• To develop a new method, the Jarzynski matrix equality (JME), for free-energy calculations from nonequilibrium trajectories.

Main Methods:

• Developed the Jarzynski matrix equality (JME) method.
• Applied JME to analyze nonequilibrium trajectories connecting metastable conformational regions.
• Validated JME using toy models, Lennard-Jones fluids, and polymer chain models.

Main Results:

• The JME method successfully estimates local free energies from nonequilibrium trajectories.
• Demonstrated satisfactory accuracy in free-energy calculations across various model systems.
• Showcased the ability to estimate free energy from arbitrary initial distributions.

Conclusions:

• The JME method significantly broadens the applicability of nonequilibrium techniques for free-energy calculations.
• This advancement is particularly valuable for complex systems where initial equilibrium states are challenging to achieve.
• JME offers a powerful tool for simulating and experimenting with complex thermodynamic systems.