Force–Extension Curve
Key physics: FJC elasticity is purely entropic — no bond stretching. Force aligns segments against thermal disorder.
Langevin function: ⟨x/L₀⟩ = coth(fb/k_BT) − k_BT/fb
At small forces: linear spring with k = 3k_BT/(Nb²)
At large forces: approaches full extension as 1 − k_BT/(fb)