Theory of nonequilibrium multicomponent coexistence.

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Soft Matter Physics

Background:

• Multicomponent phase separation is common in biological and synthetic systems.
• Equilibrium thermodynamics defines phase boundaries but is insufficient for nonequilibrium systems.
• A need exists for a nonequilibrium theory to describe phase coexistence in complex systems.

Purpose of the Study:

• To develop a mechanical theory for multicomponent phase coexistence outside of equilibrium.
• To generalize equilibrium concepts like chemical potential and thermodynamic pressure to nonequilibrium states.
• To establish a foundational framework for understanding high-dimensional nonequilibrium phase transitions.

Main Methods:

• Development of a mechanical theory for coexistence criteria.
• Generalization of equilibrium state functions (chemical potential, thermodynamic pressure) to nonequilibrium.
• Numerical verification using the phenomenological multicomponent active model B+.

Main Results:

• A mechanical theory for multicomponent coexistence was established.
• Coexistence criteria were formulated as equalities of generalized state functions.
• The existence of these generalized notions was numerically confirmed for various systems.

Conclusions:

• The developed theory provides a novel mechanical approach to multicomponent phase coexistence.
• It extends traditional thermodynamic concepts to nonequilibrium scenarios.
• This work lays the groundwork for a comprehensive theory of nonequilibrium phase transitions.