First-principles superadiabatic theory for the dynamics of inhomogeneous fluids

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.

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• Comparative study of force-based classical density functional theory
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• Reduced-variance orientational distribution functions from torque sampling
• Superadiabatic dynamical density functional study of Brownian hard-spheres in time-dependent external potentials
• Combining integral equation closures with force density functional theory for the study of inhomogeneous fluids
• Dynamic Density Functional Theory with Inertia and Background Flow
• Superadiabatic dynamical density functional theory for colloidal suspensions under homogeneous steady-shear
• Routes to the density profile and structural inconsistency
• Dynamical field theories for biaxial liquid crystals