Diffusion process in a deterministically forced flow

TL;DR

This paper investigates when microscopic particle dynamics under deterministic forcing can be modeled as Markovian diffusion, distinguishing between forces acting selectively on particles and those disturbing the medium.

Contribution

It provides a detailed analysis of conditions under which deterministic stirring leads to a Markovian diffusion description, clarifying the role of different force types.

Findings

Differentiates between forces that act on particles and those that disturb the medium.

Identifies conditions for microscopic dynamics to be interpreted as diffusion.

Highlights the impact of deterministic stirring on diffusion processes.

Abstract

We analyze circumstances under which the microscopic dynamics of particles which are driven by a forced, gradient-type flow can be consistently interpreted as a Markovian diffusion process. Special attention is paid to discriminating between forces that are presumed to act selectively upon diffusing particles, while leaving the random medium statistically at rest (Smoluchowski diffusion processes), and those perturbing the random medium itself and thus creating the nontrivial flows. We focus on the deterministic "stirring" scenarios.