The fluctuation-dissipation relation holds for a macroscopic tracer in an active bath

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Soft Matter Physics

Background:

• The fluctuation-dissipation relation (FDR) is a cornerstone of equilibrium statistical mechanics, connecting fluctuations and dissipation.
• Extending FDR beyond equilibrium is crucial for developing a broader understanding of non-equilibrium thermodynamics.
• Previous extensions often require specific system conditions and lack general applicability.

Purpose of the Study:

• To experimentally investigate the validity of a generalized fluctuation-dissipation relation (FDR) in a non-equilibrium system.
• To explore the applicability of the generalized FDR across a wide range of dynamic regimes.
• To identify the underlying physical mechanisms governing the generalized FDR in active systems.

Main Methods:

• Utilizing a harmonically trapped tracer particle interacting with self-propelled walkers.
• Experimentally controlling and analyzing the dynamics of the tracer across underdamped and critically damped regimes.
• Measuring and correlating active fluctuations and energy dissipation within the system.

Main Results:

• Demonstrated experimental evidence for a generalized FDR in the studied active system.
• Confirmed the validity of the generalized FDR across a broad spectrum of active fluctuation frequencies.
• Observed that the system's dynamics, from underdamped to critically damped, adhere to the generalized FDR.

Conclusions:

• A generalized FDR is experimentally validated for active systems, specifically with a tracer interacting with self-propelled walkers.
• The generalized FDR's robustness across different dynamic regimes suggests a universal applicability under certain conditions.
• A single dominant channel for energy input and dissipation is identified as the key factor enabling the generalized FDR's validity in this active system.