Towards a computational chemical potential for nonequilibrium steady-state systems

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Computational Chemistry

Background:

• Chemical potential is crucial for understanding phase transitions and material properties.
• Existing methods for calculating chemical potential are limited to equilibrium systems.
• Systems far from equilibrium present unique challenges for thermodynamic property calculations.

Purpose of the Study:

• To develop a computable analog of chemical potential for systems under steady-state non-equilibrium conditions.
• To extend the applicability of chemical potential calculations to systems beyond thermodynamic equilibrium.
• To provide theoretical and numerical tools for studying non-equilibrium phenomena.

Main Methods:

• Adapted Widom's insertion method, commonly used for equilibrium fluids.
• Derived two distinct formulas: one for steady-state and one for the transient region.
• Utilized theoretical reasoning and numerical evidence to support the proposed approach.

Main Results:

• Introduced a novel, albeit approximate, formula for chemical potential in steady-state non-equilibrium systems.
• Developed a second formula applicable to the transient phase of non-equilibrium systems.
• Demonstrated the numerical feasibility and presented representative calculations for the transient approach.

Conclusions:

• The proposed method offers a viable, though approximate, route to calculating chemical potential in non-equilibrium systems.
• The derived formulas provide valuable insights into the behavior of systems far from equilibrium.
• Further research can refine the accuracy and expand the applications of this non-equilibrium chemical potential analog.