  We present a generalization of the Green-Kubo expressions for thermal
transport coefficients $\mu$ in complex fluids of the generic form, $\mu=
\mu_\infty +\int^\infty_0 dt V^{-1} < J_\epsilon \exp(t {\cal L}) J >_0$, i.e.
a sum of an instantaneous transport coefficient $\mu_\infty$, and a time
integral over a time correlation function in a state of thermal equilibrium
between a current $J$ and a transformed current $J_\epsilon$. The streaming
operator $\exp(t{\cal L})$ generates the trajectory of a dynamical variable
$J(t) =\exp(t{\cal L}) J$ when used inside the thermal average $<...>_0$. These
formulas are valid for conservative, impulsive (hard spheres), stochastic and
dissipative forces (Langevin fluids), provided the system approaches a thermal
equilibrium state. In general $\mu_\infty \neq 0$ and $J_\epsilon \neq J$,
except for the case of conservative forces, where the equality signs apply. The
most important application in the present paper is the hard sphere fluid.
