  For a given thermodynamic system, and a given choice of coarse-grained state
variables, the knowledge of a force-flux constitutive law is the basis for any
nonequilibrium modeling. In the first paper of this series we established how,
by a generalization of the classical fluctuation-dissipation theorem (FDT), the
structure of a constitutive law is directly related to the distribution of the
fluctuations of the state variables. When these fluctuations can be expressed
in terms of diffusion processes, one may use Green-Kubo-type coarse-graining
schemes to find the constitutive laws. In this paper we propose a
coarse-graining method that is valid when the fluctuations are described by
means of general Markov processes, which include diffusions as a special case.
We prove the success of the method by numerically computing the constitutive
law for a simple chemical reaction $A \rightleftarrows B$. Furthermore, we show
that one cannot find a consistent constitutive law by any Green-Kubo-like
scheme.
