  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.
