  We investigate the role of fluctuations in single molecule measurements of
torque-link ($t-lk$) curves. For semiflexible polymers of finite persistence
length (i.e. polymers with contour length $L$ comparable to the persistence
length $L_P$), the torque versus link curve in the constant torque (isotorque)
ensemble is distinct from the one in the constant link (isolink) ensemble.
Thus, one encounters the conceptually interesting issue of a ``free energy of
transition'' in switching ensembles while making torque-link measurements. We
predict the dependence on the semiflexibility parameter $\beta = L/L_P$ of this
extra contribution to the free energy which shows up as an area in the
torque-link plane. This can be tested against future torque-link experiments
with single biopolymers. We bring out the inequivalence of torque-link curves
for a stiff polymer and present explicit analytical expressions for the {\it
distinct} torque-link relations in the two ensembles and the free energy
difference in switching ensembles in this context. The predictions of our work
can be tested against single molecule experiments on torsionally constrained
biopolymers.
