Three-dimensional entropic chain stiffness ($k_s=3k_{B}T/(Lb)$)

A three-dimensional ideal chain of $N$ independent segments of length $b$ has $⟨R^2⟩=N{b}^2=Lb$. The isotropic small-force susceptibility gives $⟨z⟩=F⟨R^2⟩/(3k_{B}T)$, so $k_s=3k_{B}T/(Lb)$. For a long worm-like chain, the statistical segment is $b=2l_p$. This stiffness describes entropic end-to-end extension, not axial stretching of the material backbone, whose spring constant is $EA/L$.