Confined, Active, and Steerable Matter I

We present a theoretical framework based on a Hamiltonian that models the elastic coupling between a tracer particle and the surrounding active viscoelastic biomatter. From this, we derive a generalized Langevin equation to describe the non-equilibrium mechanical response of the tracer. Our analytical expressions for the frequency-dependent tracer response function and the positional autocorrelation function align quantitatively with the available experimental data from red blood cells and actomyosin networks, both with and without adenosine triphosphate (ATP), across the entire frequency spectrum. Our model successfully reproduces the low-frequency violation of the fluctuation-dissipation theorem observed in the active systems. The extracted viscoelastic power laws, elastic constants, and effective friction coefficients from experimental data offer straightforward physical interpretations.