Linear Response Theory and Green-Kubo Relations for Active Matter

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Active Matter

Background:

• Interacting active systems exist in nonequilibrium steady states.
• Understanding their response to external perturbations is crucial.
• Detailed balance is often violated in active systems.

Purpose of the Study:

• To establish an extended fluctuation-dissipation theorem for active Brownian particles (ABP).
• To derive Green-Kubo expressions for transport coefficients.
• To quantify deviations from the Stokes-Einstein relation in active systems.

Main Methods:

• Derivation of an extended fluctuation-dissipation theorem.
• Application of a Markovian approximation.
• Computation of linear response functions using simulations.
• Comparison of analytical predictions with simulation results.

Main Results:

• An extended fluctuation-dissipation theorem for ABP was established.
• Closed Green-Kubo expressions for diffusivity and mobility were derived.
• Deviations from the Stokes-Einstein relation were quantified.
• Simulations confirmed analytical predictions for transport coefficients.

Conclusions:

• The interplay between activity and interactions is key to understanding departures from equilibrium linear response.
• The local violation of detailed balance significantly influences system dynamics.
• The developed framework provides insights into the behavior of nonequilibrium active matter.