  By considering subexponential contributions in large deviation theory, we
determine the fine structure in the probability distribution of the observable
displacement of a bead coupled to a molecular motor. More generally, for any
stochastic motion along a periodic substrate, this approach reveals a discrete
symmetry of this distribution for which hidden degrees of freedom lead to a
periodic modulation of the slope typically associated with the fluctuation
theorem. Contrary to previous interpretations of experimental data, the mean
force exerted by a molecular motor is unrelated to the long-time asymptotics of
this slope and must rather be extracted from its short-time limit.
