# Particle-conserving dynamics on the single-particle level

## TL;DR

This paper extends the particle-conserving dynamics method to binary mixtures, applying it to one-dimensional hard rods, and compares its accuracy with Brownian dynamics and density functional theory, highlighting its strengths and limitations.

## Contribution

The authors generalize particle-conserving dynamics to binary mixtures and analyze its effectiveness for one-dimensional hard rods, especially in tagged-particle dynamics.

## Key findings

- Particle-conserving dynamics outperforms dynamical density functional theory at short and intermediate times.
- The method accurately reproduces simulation data but has limitations at long times due to neglect of particle order.
- Fundamental limitations of density-based approaches are highlighted in systems with particle caging.

## Abstract

We generalize the particle-conserving dynamics method of de las Heras et al. [J. Phys. Condens. Matter: 28, 24404 (2016).] to binary mixtures and apply this to hard rods in one dimension. Considering the case of one species consisting of only one particle enables us to address the tagged-particle dynamics. The time-evolution of the species-labeled density profiles is compared to exact Brownian dynamics and (grand-canonical) dynamical density functional theory. The particle conserving dynamics yields improved results over the dynamical density functional theory and well reproduces the simulation data at short and intermediate times. However, the neglect of a strict particle order (due to the fundamental statistical assumption of ergodicity) leads to errors at long times for our one-dimensional setup. The isolated study of that error makes clear the fundamental limitations of (adiabatic) density-based theoretical approaches when applied to systems of any dimension for which particle caging is a dominant physical mechanism.