We perform a detailed analysis of both the phenomenological and analytic backgrounds 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 into account the environmental recoil effects due to locally induced tiny heat flows. By means of local expectation values we elevate the individually negligible phenomena to a non-negligible (accumulated) recoil effect on the ensemble average. The main technical input is a consequent exploitation of the Hamilton-Jacobi equation as a natural substitute for the local momentum conservation law. Together with the continuity equation (alternatively, Fokker-Planck), it forms a closed system of partial differential equations that uniquely determines an associated Markovian diffusion process. The third Newton law in the mean is utilized to generate diffusion-type processes that are either anomalous (enhanced) or generically nondispersive.

• Received 21 September 1998

DOI:https://doi.org/10.1103/PhysRevE.59.1498