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We analyzed passive particle motion in active environments using path integrals. Inertia and active noise parameters influence particle dynamics and work fluctuations, validated by a fluctuation theorem.

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Active Matter Physics

Background:

  • Understanding particle dynamics in complex environments is crucial.
  • Active environments introduce unique noise characteristics affecting passive tracers.
  • The Ornstein-Uhlenbeck process models correlated noise effectively.

Purpose of the Study:

  • To investigate the underdamped motion of a passive particle in an active environment.
  • To determine the probability distribution functions (PDFs) of position and velocity.
  • To analyze work fluctuations and validate fluctuation theorems for active systems.

Main Methods:

  • Phase space path integral method for calculating PDFs.
  • Modeling active noise using the Ornstein-Uhlenbeck process (OUP).
  • Analysis of a harmonically trapped particle with a moving trap center.

Main Results:

  • Derived PDFs for free and harmonically bound particles in an active bath.
  • Demonstrated the impact of inertia and OUP parameters on particle dynamics.
  • Investigated work fluctuations and confirmed fluctuation theorem with an effective temperature.

Conclusions:

  • The study provides insights into particle dynamics governed by active noise.
  • Inertia plays a significant role in modifying particle behavior in active media.
  • The fluctuation theorem holds for active systems, with an effective temperature characterizing the steady state.