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Asymptotic methods for confined fluids
1University of Fribourg, Department of Physics, CH-1700 Fribourg, Switzerland.
Physical Review. E
|March 19, 2025
Summary
This study introduces a method to convert grand-canonical ensemble calculations to the canonical ensemble, crucial for accurately modeling confined fluids. This approach overcomes artifacts and improves thermodynamic and microstructural predictions for small systems.
Area of Science:
- Statistical Mechanics
- Physical Chemistry
- Thermodynamics of Confined Systems
Background:
- Canonical ensemble is ideal for confined fluids with few particles, but grand-canonical is often used practically.
- Grand-canonical calculations can introduce unphysical artifacts, limiting accuracy in small systems.
Purpose of the Study:
- To develop a robust method for transforming grand-canonical observables to the canonical ensemble.
- To accurately describe the thermodynamics and microstructure of confined fluids, especially with small particle numbers.
Main Methods:
- Employing the method of asymptotics for ensemble transformation.
- Utilizing classical density functional theory for inhomogeneous fluids.
- Formulating the transformation as a contour integral in the complex fugacity plane, considering Yang-Lee zeros.
Main Results:
- Developed expansions for the canonical partition function and one-body density.
- Revealed the influence of Yang-Lee zeros on asymptotic series convergence.
- Validated the theory using an exactly soluble one-dimensional hard rod model.
Conclusions:
- The asymptotic transformation method accurately bridges grand-canonical and canonical ensembles.
- This approach enhances the reliability of theoretical models for confined fluid systems.
- The findings are applicable to systems where particle number fluctuations are significant.
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