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Asymptotic methods for confined fluids.

E Di Bernardo1, J M Brader1

  • 1University of Fribourg, Department of Physics, CH-1700 Fribourg, Switzerland.

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This summary is machine-generated.

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.

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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.