Perturbations of noise: Origins of isothermal flows

We perform a detailed analysis of both the phenomenological and analytic ba ckgrounds for the "Brownian recoil principle'' hypothesis [Phys. Rev. A 46, 4634 (1992)]. A corresponding theory of the isothermal Brownian motion of particle ensembles (Smoluchowski diffusion process approximation) takes int o account the environmental recoil effects due to locally induced tiny heat flows. By means of local expectation values we elevate the individually ne gligible phenomena to a non-negligible (accumulated) recoil effect on the e nsemble average. The main technical input is a consequent exploitation of t he Hamilton-Jacobi equation as a natural substitute for the local momentum conservation law. Together with the continuity equation (alternatively, Fok ker-Planck), it forms a closed system of partial differential equations tha t uniquely determines an associated Markovian diffusion process. The third Newton law in the mean is utilized to generate diffusion-type processes tha t are either anomalous (enhanced) or generically nondispersive.