Dynamical fluctuations of a tracer coupled to active and passive particles

Abstract

We study the induced dynamics of an inertial tracer particle elastically coupled to passive or active Brownian particles. We integrate out the environment degrees of freedom to obtain generalized Langevin equation for the tracer dynamics in both cases. In particular, we find the exact form of the dissipation kernel and effective noise experienced by the tracer and compare it with the phenomenological modeling of active baths used in previous studies. We show that the second fluctuation-dissipation relation (FDR) does not hold at early times for both cases. However, at finite times, the tracer dynamics violate (obeys) the FDR for the active (passive) environment. We calculate the linear response formulas in this regime for both cases and show that the passive medium satisfies an equilibrium fluctuation response relation (FRR), while the active medium does not -- we quantify the extent of this violation explicitly. We show that though the active medium generally renders a nonequilibrium description of the tracer, an effective equilibrium picture emerges asymptotically in the small activity limit of the medium. We also calculate the mean squared velocity and mean squared displacement of the tracer and report how they vary with time.

21 pages. Comments are welcome

References in corpus (15)

• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Generalized energy equipartition in harmonic oscillators driven by active baths
• Fluctuations and Rheology in Active Bacterial Suspensions
• Entropy production of active particles and for particles in active baths
• Active and Nonlinear Microrheology in Dense Colloidal Suspensions
• Intermediate scattering function of an anisotropic active Brownian particle
• Effects of active fluctuations on energetics of a colloidal particle: superdiffusion, dissipation and entropy production
• The Parental Active Model: a unifying stochastic description of self-propulsion
• Interacting Brownian dynamics in a nonequilibrium particle bath
• Energetics of active fluctuations in living cells
• Time-dependent properties of interacting active matter: dynamical behavior of one-dimensional systems of self-propelled particles
• How statistical forces depend on thermodynamics and kinetics of driven media
• Activity driven transport in harmonic chains
• A Brownian cyclic engine operating in a viscoelastic active suspension
• Passive particle in an active bath: How can we tell it is out of equilibrium?

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• Universal Poisson statistics of a passive tracer diffusing in dilute active suspensions
• Harmonic chain driven by active Rubin bath: transport properties and steady-state correlations
• Tracer dynamics in an interacting active bath: fluctuations and energy partition
• A Cold Tracer in a Hot Bath: In and Out of Equilibrium
• Statistical mechanics of a cold tracer in a hot bath
• Stationary state of harmonic chains driven by boundary resetting
• Recoil of a driven tracer in a correlated medium