Perturbations of Noise: The origins of Isothermal Flows

TL;DR

This paper investigates the origins of isothermal flows by analyzing environmental recoil effects in Brownian motion, using a PDE system based on Hamilton-Jacobi and Fokker-Planck equations to describe diffusion processes.

Contribution

It introduces a novel theoretical framework linking recoil effects to isothermal Brownian motion through a PDE system involving Hamilton-Jacobi and continuity equations.

Findings

Recoil effects can significantly influence Brownian motion behavior.

The PDE framework predicts anomalous and non-dispersive diffusion processes.

A new connection between local heat flows and ensemble dynamics is established.

Abstract

We make a detailed analysis of both phenomenological and analytic background for the "Brownian recoil principle" hypothesis (Phys. Rev. A 46, (1992), 4634). A corresponding theory of the isothermal Brownian motion of particle ensembles (Smoluchowski diffusion process approximation), gives account of 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 which uniquely determines an associated Markovian diffusion process. The third Newton law in the mean is utilised to generate diffusion-type processes which are either anomalous (enhanced), or generically non-dispersive.