Entropic Hooke law for a one-dimensional chain
= Entropic Hooke law for a one-dimensional chain
The physical tension is $f=k_BT\tau$. At small extension,
$$
f\sim\frac{k_BT}{na^2}L.
$$
At fixed tension the extension is $L=na\tanh(fa/(k_BT))$ and decreases as temperature rises.