Diffusion of a tracer in a dense mixture of soft particles connected to different thermostats

TL;DR

This paper derives an analytical expression for the self-diffusion coefficient of a tracer in a dense, soft particle mixture connected to different thermostats, validated by simulations, with implications for biological media.

Contribution

It extends previous models to include tracers in contact with multiple baths and provides a general analytical framework for diffusion in linear, fluctuating environments.

Findings

Analytical expression matches Brownian dynamics simulations.

Tracer diffusivity is influenced by the activity of the dense environment.

Results applicable to biological media and various fluctuating environments.

Abstract

We study the dynamics of a tracer in a dense mixture of particles connected to different thermostats. Starting from the overdamped Langevin equations that describe the evolution of the system, we derive the expression of the self-diffusion coefficient of a tagged particle in the suspension, in the limit of soft interactions between the particles. Our derivation, which relies on the linearization of the Dean-Kawasaki equations obeyed by the density fields and on a path-integral representation of the dynamics of the tracer, extends previous derivations that held for tracers in contact with a single bath. Our analytical result is confronted to results from Brownian dynamics simulations. The agreement with numerical simulations is very good even for high densities. We show how the diffusivity of tracers can be affected by the activity of a dense environment of soft particles that may represent polymer coils -- a result that could be of relevance in the interpretation of measurements of diffusivity in biological media. Finally, our analytical result is general and can be applied to the diffusion of tracers coupled to different types of fluctuating environments, provided that their evolution equations are linear and that the coupling between the tracer and the bath is weak.