Nonequilibrium mode-coupling theory for dense active systems of self-propelled particles

Area of Science:

• Statistical Physics
• Soft Matter Physics
• Biophysics

Background:

• Active matter systems, composed of self-propelled particles, are crucial in biological contexts and present complex physics challenges.
• Understanding dense liquid states of active matter requires advanced theoretical frameworks beyond traditional equilibrium statistical mechanics.

Purpose of the Study:

• To develop a nonequilibrium mode-coupling theory (MCT) for dense active matter systems.
• To investigate the effective temperature and relaxation dynamics of self-propelled particles.
• To analyze the influence of activity parameters on system behavior near a glass transition.

Main Methods:

• Developed an extended nonequilibrium mode-coupling theory (MCT) incorporating colored noise for particle activity.
• Utilized a generalized fluctuation-dissipation theorem to compute the effective temperature (Teff).
• Performed scaling analysis near the MCT glass transition point to determine the behavior of the alpha-relaxation time (τα).

Main Results:

• Calculated a time-dependent effective temperature (Teff) that reaches a constant long-time limit dependent on activity parameters (self-propulsion force f0 and persistence time τp).
• Found that the long-time limit of Teff is phenomenologically captured by the potential energy of a single, trapped active particle (STAP).
• Demonstrated that the alpha-relaxation time (τα) scales with the self-propulsion force as τα ∼ f0^(-2γ), where γ is the MCT exponent for passive systems.

Conclusions:

• The nonequilibrium nature of active matter significantly impacts its thermodynamic and dynamic properties.
• The developed MCT framework provides a robust tool for studying active systems, accurately predicting behavior near glass transitions.
• Scaling laws derived from MCT show universal behavior governed by the passive system's exponent, despite variations in relaxation times with persistence time.