Third Newton Law in the Mean and Perturbations of Noise

We analyze an isothermal Brownian motion of particle ensembles in the Smoluchowski approximation. Contrary to standard procedures, the environmental recoil effects associated with locally induced heat flows are not completely disregarded. The main technical tool in the study of such weakly-out-of equilibrium systems is a consequent exploitation of the Hamilton-Jacobi equation. The third Newton law in the mean is utilised to generate diffusion-type processes which are either anomalous (enhanced), or generically non-dispersive.