  Dynamical density functional theory (DDFT) is a powerful variational
framework to study the nonequilibrium properties of colloids by only
considering a time-dependent one-body number density. Despite the large number
of recent successes, properly modeling the long-time dynamics in interacting
systems within DDFT remains a notoriously difficult problem, since structural
information, accounting for temporary or permanent particle cages, gets lost.
Here we address such a caging scenario by reducing it to a clean
one-dimensional problem, where the particles are naturally ordered (arranged on
a line) by perfect cages created by their two next neighbors. In particular, we
construct a DDFT approximation based on an equilibrium system with an
asymmetric pair potential, such that the corresponding one-body densities still
carry the footprint of particle order. Applied to a system of confined hard
rods, this order-preserving dynamics (OPD) yields exact results at the system
boundaries, in addition to the imprinted correct long-time behavior of density
profiles representing individual particles. In an open system, our approach
correctly reproduces the reduced long-time diffusion coefficient and
subdiffusion, characteristic for a single-file setup. These observations cannot
be made using current forms of DDFT without particle order.
