  We analyze the statistics of work generated by a gradient flow to stretch a
nonlinear polymer. We obtain the Large Deviation Function (LDF) of the work in
the full range of appropriate parameters by combining analytical and numerical
tools. The LDF shows two distinct asymptotes: "near tails" are linear in work
and dominated by coiled polymer configurations, while "far tails" are quadratic
in work and correspond to preferentially fully stretched polymers. We find the
extreme value statistics of work for several singular elastic potentials, as
well as the mean and the dispersion of work near the coil-stretch transition.
The dispersion shows a maximum at the transition.
