  We present generalized Green-Kubo expressions for thermal transport
coefficients $\mu$ in non-conservative fluid-type systems, of the generic form,
$\mu$ $= \mu_\infty$ $+\int^\infty_0 dt V^{-1} \av{I_\epsilon \exp(t {\cal L})
I}_0$ where $\exp(t{\cal L})$ is a pseudo-streaming operator. It consists of 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 $I$ and its conjugate current $I_\epsilon$. This formula with
$\mu_\infty \neq 0$ and $I_\epsilon \neq I$ covers vastly different systems,
such as strongly repulsive elastic interactions in hard sphere fluids, weakly
interacting Langevin fluids with dissipative and stochastic interactions
satisfying detailed balance conditions, and "the likes", defined in the text.
For conservative systems the results reduce to the standard formulas.
