Fluctuation-dissipation in active matter

Area of Science:

• Colloidal science
• Soft matter physics
• Statistical mechanics

Background:

• The fluctuation-dissipation theorem (FDT) connects equilibrium thermal fluctuations to a system's response to external forces.
• The Stokes-Einstein-Sutherland (SES) relation quantifies this for passive colloidal suspensions.
• Active suspensions, being far from equilibrium, may violate FDT due to nonthermal internal stresses.

Purpose of the Study:

• To derive a general relationship between diffusivity and mobility in colloidal suspensions beyond equilibrium conditions.
• To identify conditions under which the FDT holds in generic colloidal systems.
• To quantify FDT deviations in active Brownian particles (ABPs) and propose an effective SES relation.

Main Methods:

• Generalized Taylor dispersion theory was employed to analyze particle dynamics.
• Analysis focused on the relationship between particle diffusivity (fluctuation) and mobility (dissipation).
• Specific conditions for FDT validity were derived, and deviations in ABPs were quantified.

Main Results:

• A general relationship between diffusivity and mobility was established for non-equilibrium colloidal suspensions.
• Conditions for the FDT to hold were derived, revealing they may not be met even in simple ABP systems.
• Deviations from FDT in ABPs were quantified and expressed via an effective SES relation.

Conclusions:

• The FDT, while fundamental for equilibrium systems, requires careful consideration in active suspensions.
• Active Brownian particles can exhibit deviations from the FDT due to their inherent energy conversion.
• An effective SES relation can be formulated to describe the dynamics of active suspensions, incorporating their unique properties.