1998/09/22 by Piotr Garbaczewski · 1 citation
Chemistry · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Anomalous diffusion #Brownian motion #Classical mechanics #Differential equation #Diffusion #Diffusion process #Fokker–Planck equation #Isothermal process #Langevin equation #Momentum (technical analysis) #Physics #Quantum mechanics #Recoil #Smoluchowski coagulation equation #Statistical physics #Stochastic differential equation #Thermodynamics #chao-dyn #cond-mat #nlin.CD #quant-ph #stochastic dynamics and bifurcation #thermodynamics and calorimetric analyses
paper · pdf · doi:10.1103/physreve.59.1498
published as Phys. Rev. E 59, (1999), 1498--1511 · Latex file
arxiv created 1998/09/22 · openalex publication_date 1999/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.