Freely-jointed chain; F = 3kT·R/(Nb²); Gaussian end-to-end distribution
An ideal polymer chain of N segments of length b has mean-square end-to-end distance ⟨R²⟩ = Nb². The entropic spring constant k_spring = 3kT/(Nb²) arises because stretching reduces conformational entropy. The worm-like chain (WLC) model captures DNA stiffness via persistence length Lp ≈ 50 nm.