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 dense interacting odd-diffusive fluids and apply it to ultrasoft particles in two dimensions. In bulk, odd diffusion qualitatively reshapes collective relaxation by generating transient circulating current patterns which do not exist in normal fluids. Under harmonic ring confinement, the circulation of 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.

💡 Research Summary

In this work the authors develop a dynamical density functional theory (DDFT) that incorporates odd (antisymmetric) diffusion for dense interacting fluids. Starting from the many‑body Smoluchowski equation, they integrate out all but one particle to obtain the continuity equation for the one‑body density ρ(r,t). Because the resulting current still depends on the two‑body density, they close the hierarchy using the standard DDFT adiabatic approximation: the instantaneous non‑equilibrium system is mapped onto an equilibrium system with the same density profile, allowing the definition of a local chemical potential μ(r,t)=δF