3D illustration depicting the primitive path of a test polymer (red line) confined within an effective tube formed by surrounding self-propelled polymers at various times t. In the equilibrium state (t = 0), a combination of strong entanglement points (A, C, and D) and weak entanglement points (B) coexists, with strong entanglements distinguished by the presence of hairpin structures. Due to the activity, before reaching the steady state t ≳ L / v, the number of strong entanglement points increases (as shown by the yellow polymer wrapping around the red polymer at point B), leading to the elongation of the primitive path. The direction of self-propulsion is indicated by colored arrows, while the distance between successive entanglement points defines the entanglement length N e.
