Memory effect and fluctuating anomalous dynamics of a tagged monomer

We analyze the anomalous dynamics of a tagged monomer under external navigation. The memory effect causing the anomaly is elucidated, which depends on the magnitude of the force. In particular, the nonlinear and nonequilibrium memory effect under strong force is characterized by the force-dependent self-affine process for the tension transmission along the connectivity. Utilizing such knowledge, a generalized Langevin equation approach is proposed to quantify the fluctuating dynamics of driven anomalous walkers.