Dynamical Density Functional Theory for Dense Odd-Diffusive Fluids

Odd diffusion breaks time-reversal symmetry in overdamped systems through transverse probability currents while preserving equilibrium steady states. In this work, we develop a dynamical density functional theory (DDFT) for densely interacting odd-diffusive fluids and apply it to ultrasoft particles in two dimensions. In the bulk, odd diffusion qualitatively reshapes collective relaxation by generating transient circulating current patterns that do not exist in normal fluids. Under harmonic ring confinement, the circulation of the probability current induces an angular redistribution of density along the ring during relaxation. This unique footprint of odd diffusion opens up a shorter pathway to equilibrium. Repulsive interactions significantly enhance these effects. Excellent agreement with Brownian dynamics simulations confirms that our odd-DDFT framework quantitatively captures all essential nonequilibrium aspects of the nontrivial odd transport and collective redistribution for dense fluids in both bulk and confined geometries.