Trapped tracer in a non-equilibrium bath: dynamics and energetics

We study the dynamics of a tracer that is elastically coupled to active particles being kept at two different temperatures, as a prototype of tracer dynamics in a non-equilibrium bath. Employing analytical techniques, we find the exact solution of the probability density function for the effective motion of the tracer. The analytical results are supported by numerical simulations. By combining the experimentally accessible quantities such as the response function and the power spectrum, we measure the non-equilibrium fluctuations in terms of the effective temperature. In addition, we compute the energy dissipation rate to find the precise effects of activity. Our study is relevant in understanding athermal fluctuations arising in cytoskeletal networks or inside a chromosome. We study the dynamics of a tracer that is elastically coupled to active particles being kept at two different temperatures, as a prototype of tracer dynamics in a non-equilibrium bath.