Classical statistical mechanics in the μVL and μpR ensembles

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Computational Chemistry

Background:

• Thermodynamic properties are crucial for understanding molecular systems.
• Existing methods for calculating entropy derivatives have limitations in certain ensembles.
• The adiabatic grand-isochoric (μVL) and adiabatic grand-isobaric (μpR) ensembles are important for specific thermodynamic conditions.

Purpose of the Study:

• To systematically derive molecular expressions for thermodynamic properties and entropy derivatives up to third order.
• To extend Lustig's methodology to the adiabatic grand-isochoric (μVL) and adiabatic grand-isobaric (μpR) ensembles.
• To validate the derived expressions using computational simulations.

Main Methods:

• Utilized Lustig's methodology for deriving molecular expressions.
• Developed phase-space functions representing entropy derivatives with respect to chemical potential, volume, and Hill energy (μVL ensemble).
• Developed phase-space functions representing entropy derivatives with respect to chemical potential, pressure, and Ray energy (μpR ensemble).

Main Results:

• Successfully derived molecular expressions for thermodynamic properties and entropy derivatives in the μVL and μpR ensembles.
• The derived expressions were validated through Monte Carlo simulations.
• The Lennard-Jones model fluid was used as a test case, showing good agreement between theory and simulation.

Conclusions:

• The derived molecular expressions provide a robust framework for calculating thermodynamic properties and entropy derivatives in adiabatic ensembles.
• The methodology is applicable to various systems and conditions, enhancing theoretical understanding.
• The validation confirms the accuracy and utility of the new expressions for molecular simulations.