Particle-conserving dynamics on the single-particle level

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.