Inertial particle under active fluctuations: Diffusion and work distributions

We study the underdamped motion of a passive particle in an active environment. Using the phase space path integral method we find the probability distribution function of position and velocity for a free and a harmonically bound particle. The environment is characterized by an active noise which is described as the Ornstein-Uhlenbeck process (OUP). Taking two similar, yet slightly different OUP models, it is shown how inertia along with other relevant parameters affect the dynamics of the particle. Further we investigate the work fluctuations of a harmonically trapped particle by considering the trap center being pulled at a constant speed. Finally, the fluctuation theorem of work is validated with an effective temperature in the steady-state limit.

Automated summary

We study the underdamped motion of a passive particle in an active environment using the phase space path integral method. The probability distribution function of position and velocity for a free and a harmonically bound particle is derived. Two similar OUP models are considered to investigate the effects of inertia and other parameters on the particle dynamics. The work fluctuations of a harmonically trapped particle are also analyzed, and the fluctuation theorem of work is validated with an effective temperature in the steady-state limit.