  The unique fluctuation-dissipation theorem for equilibrium stands in contrast
with the wide variety of nonequilibrium linear response formulae. Their most
traditional approach is "analytic", which, in the absence of detailed balance,
introduces the logarithm of the stationary probability density as observable.
The theory of dynamical systems offers an alternative with a formula that
continues to work when the stationary distribution is not smooth. We show that
this method works equally well for stochastic dynamics, and we illustrate it
with a numerical example for the perturbation of circadian cycles. A second
"probabilistic" approach starts from dynamical ensembles and expands the
probability weights on path space. This line suggests new physical questions,
as we meet the frenetic contribution to linear response, and the relevance of
the change in dynamical activity in the relaxation to a (new) nonequilibrium
condition.
