First-principles superadiabatic theory for the dynamics of inhomogeneous fluids

TL;DR

This paper introduces a superadiabatic dynamical density functional theory for inhomogeneous fluids out-of-equilibrium, explicitly incorporating two-body correlations to improve the accuracy of density relaxation predictions.

Contribution

It develops a superadiabatic DDFT that explicitly includes two-body correlation dynamics, advancing the understanding of nonequilibrium fluid behavior beyond standard adiabatic approaches.

Findings

Superadiabatic forces are crucial for accurate density dynamics.

The theory predicts slower relaxation than standard DDFT.

Improved agreement with Brownian dynamics simulations.

Abstract

For classical many-body systems subject to Brownian dynamics we develop a superadiabatic dynamical density functional theory (DDFT) for the description of inhomogeneous fluids out-of-equilibrium. By explicitly incorporating the dynamics of the inhomogeneous two-body correlation functions we obtain superadiabatic forces directly from the microscopic interparticle interactions. We demonstrate the importance of these nonequilibrium forces for an accurate description of the one-body density by numerical implementation of our theory for three-dimensional hard-spheres in a time-dependent planar potential. The relaxation of the one-body density in superadiabatic-DDFT is found to be slower than that predicted by standard adiabatic DDFT and significantly improves the agreement with Brownian dynamics simulation data. We attribute this improved performance to the correct treatment of structural relaxation within the superadiabatic-DDFT. Our approach provides fundamental insight into the underlying structure of dynamical density functional theories and makes possible the study of situations for which standard approaches fail.