= Solution
If a physical tension $f$ acts on a state of extension $l_i$, its mechanical energy is $-fl_i$. The <canonical ensemble> therefore assigns that state the <Boltzmann factor>
$$
e^{-(-fl_i)/(k_BT)}=e^{fl_i/(k_BT)}.
$$
Comparison with the statistical weight $e^{\tau l_i}$ gives
$$
\boxed{\tau=\frac{f}{k_BT}},
\qquad
\boxed{f=k_BT\tau}.
$$
Equivalently, $f$ is the <thermodynamic conjugate variable> to $L$ in the <Gibbs free energy>, just as pressure is conjugate to volume.
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