Towards bulk thermodynamics via non-equilibrium methods: gaseous methane as a case study

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Computational Chemistry

Background:

• The Jarzynski equality (JE) is a powerful tool for calculating free energy landscapes in molecular systems under non-equilibrium conditions.
• Existing methods often focus on molecular-sized systems and steered transformations.
• Deriving equations of state for bulk materials typically relies on equilibrium statistical mechanics.

Purpose of the Study:

• To demonstrate the application of the Jarzynski equality (JE) for deriving equations of state for bulk thermodynamic systems.
• To bridge non-equilibrium methods with traditional thermodynamics for macroscopic properties.
• To establish a computational framework for calculating equations of state from first principles.

Main Methods:

• Physically framing the
• total energy morphing
• computational strategy as a build-up from an ideal state to a real thermodynamic state.
• Utilizing the Jarzynski equality machinery to compute excess free energy as a function of controlled state variables.
• Evaluating thermodynamic derivatives of the excess free energy to obtain the equation of state.

Main Results:

• Successfully derived the equation of state for gaseous methane.
• Demonstrated the calculation of Helmholtz free energy versus particle density at fixed temperature.
• Showcased the thermodynamic derivative calculation with respect to volume.

Conclusions:

• The Jarzynski equality and "total energy morphing" provide a viable non-equilibrium pathway to determine bulk material equations of state.
• This approach offers a new perspective for investigating the thermodynamics of extended systems.
• The methodology is adaptable for studying diverse materials and thermodynamic conditions.