One-dimensional freely jointed chain

This is the one-dimensional version of a freely jointed chain, an ideal chain. A chain of $n$ links of length $a$, each pointing independently right or left, has extensionand multiplicity $n!/(n_{+}!n_{-}!)$.

Weighting each configuration by $e^{\tau l}$ gives

The physical tension is $f=k_{B}T\tau$. At small extension,At fixed tension the extension is $L=na\tanh (fa/(k_{B}T))$ and decreases as temperature rises.