Using bijective maps to improve free-energy estimates.

Area of Science:

• Statistical mechanics
• Thermodynamics
• Computational physics

Background:

• Estimating free-energy differences is crucial in various scientific domains.
• Existing methods often require significant computational resources or specific sampling techniques.

Purpose of the Study:

• To derive a fluctuation theorem for generalized work distributions.
• To develop a robust maximum likelihood estimator for free-energy differences.
• To apply this method to calculate the chemical potential of a Lennard-Jones fluid.

Main Methods:

• Derivation of a fluctuation theorem based on bijective mappings of phase spaces.
• Development of a two-sided constrained maximum likelihood estimator.
• Utilizing equilibrium samples from both systems for estimation.
• Application to a dense Lennard-Jones fluid model.

Main Results:

• The derived fluctuation theorem provides a theoretical foundation for the estimator.
• The maximum likelihood estimator demonstrates effectiveness in calculating free-energy differences.
• Accurate evaluation of the chemical potential for the Lennard-Jones fluid was achieved.
• Analysis of map construction and performance provided insights into the method's applicability.

Conclusions:

• The novel fluctuation theorem and associated estimator offer an efficient approach for free-energy calculations.
• This method enhances the accuracy and applicability of thermodynamic property estimations.
• The study provides a valuable tool for computational physics and chemistry research.