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Updated: Oct 23, 2025
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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Classical statistical mechanics in the grand canonical ensemble
Philipp Ströker1, Karsten Meier1
1Institut für Thermodynamik, Helmut-Schmidt-Universität/Universität der Bundeswehr Hamburg, Holstenhofweg 85, 22043 Hamburg, Germany.
Physical Review. E
|August 20, 2021
Summary
Researchers derived new expressions for calculating thermodynamic properties of fluids in the grand canonical ensemble. These phase-space functions offer more reliable results for properties like isothermal compressibility, validated by simulations.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Computational Chemistry
Background:
- Thermodynamic properties are crucial for understanding fluid behavior.
- Existing methods for the grand canonical ensemble have limitations.
- Lustig's methodology provides a robust framework for ensemble calculations.
Purpose of the Study:
- To derive rigorous expressions for thermodynamic properties in the grand canonical ensemble.
- To extend Lustig's methodology to the grand canonical ensemble.
- To validate the new expressions using the Lennard-Jones model fluid.
Main Methods:
- Application of Lustig's methodology to the grand canonical ensemble.
- Expressing thermodynamic properties via phase-space functions.
- Utilizing Monte Carlo simulations for validation.
- Deriving expressions for temperature-dependent potentials for quantum corrections.
Main Results:
- Rigorous expressions for thermodynamic properties derived in terms of phase-space functions.
- Phase-space functions involve ensemble averages of particle number, potential energy, and its volume derivatives.
- Validated expressions show improved accuracy for thermal expansion coefficient, isothermal compressibility, and thermal pressure coefficient compared to literature.
- Demonstrated equivalence to canonical ensemble expressions in the thermodynamic limit.
Conclusions:
- The derived expressions provide a more reliable method for calculating thermodynamic properties of fluids in the grand canonical ensemble.
- The phase-space functions offer a unified approach applicable to both classical and semiclassical simulations.
- The results align well with accurate equations of state for model fluids like Lennard-Jones.
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