  An equilibrium system which is perturbed by an external potential relaxes to
a new equilibrium state, a process obeying the fluctuation-dissipation theorem.
In contrast, perturbing by nonconservative forces yields a nonequilibrium
steady state, and the fluctuation-dissipation theorem can in general not be
applied. Here we exploit a freedom inherent to linear response theory: Force
fields which perform work that does not couple statistically to the considered
observable can be added without changing the response. Using this freedom, we
demonstrate that the fluctuation-dissipation theorem can be applied for certain
nonconservative forces. We discuss the case of a nonconservative force field
linear in particle coordinates, where the mentioned freedom can be formulated
in terms of symmetries. In particular, for the case of shear, this yields a
response formula, which we find advantageous over the known Green-Kubo relation
in terms of statistical accuracy.
