Continuously perturbed equivalent classes of asymptotically stable kinetic equations

In this paper, the second in a series, it is shown how under linear Langevin perturbations the information contained in a stability constraint specification involving a quadratic kinetic potential determines, for the equivalent class of flux (rate) equations it generates, a conjugate potential which, together with the spectral properties of the random term, serves to characterize completely the stationary probability distribution, the static and time autocorrelations of the components of the macrovariable defining the process, the linear response function for these components and the associated fluctuation-dissipation theorem. The equivalent classes generated by quadratic kinetic potentials under linear vector-valued Langevin perturbations exhaust the entire class of multidimensional stationary Gaussian-Markov processes for which the underlying unperturbed flux equations are globally asymptotically stable.