Position-dependent and pair diffusivity profiles from steady-state solutions of color reaction-counterdiffusion problems

TL;DR

This paper presents a method to directly determine position-dependent and pair diffusivity profiles in condensed phases using steady-state solutions of the Smoluchowski equation combined with equilibrium trajectory data, avoiding complex inference techniques.

Contribution

It introduces a novel approach that leverages steady-state solutions and equilibrium data to obtain diffusivity profiles without Bayesian inference or time-dependent analysis.

Findings

Enables direct calculation of diffusivity profiles from steady-state data

Eliminates need for Bayesian inference or likelihood maximization

Applicable to molecular simulations and microscopy data

Abstract

We show how the steady-state solution of the Smoluchowski (Fokker-Planck) equation for a color reaction-counterdiffusion problem, together with equilibrium trajectory information (e.g., from molecular simulations or confocal microscopy experiments), can be used to determine position-dependent or pair diffusivity profiles for condensed phases directly without the need for Bayesian inference, likelihood maximization, or the analysis of time-dependent data.