Perspective: How to overcome dynamical density functional theory

Abstract

We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory. Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As~a~demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of dynamical density functional theory as well as the limited availability of its analytical functional approximations.

21 pages, 5 figures. J. Phys.: Condens. Matter (invited Perspective)

References in corpus (40)

• Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Non-equilibrium sedimentation of colloids on the particle scale
• Iterative Reconstruction of Memory Kernels
• The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics
• Dynamical density functional theory for dense atomic liquids
• A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids
• Primitive Model Electrolytes in the Near and Far Field: Decay Lengths from DFT and Simulations
• Non-adiabatic electron dynamics in time-dependent density-functional theory
• Inverse Design for Self Assembly via On-the-Fly Optimization
• Non-negative Interfacial Tension in Phase-Separated Active Brownian Particles
• Phase coexistence of active Brownian particles
• Superadiabatic forces in Brownian many-body dynamics
• Machine-learning free-energy functionals using density profiles from simulations
• Analytical classical density functionals from an equation learning network
• Molecular dynamics of open systems: construction of a mean-field particle reservoir
• Density depletion and enhanced fluctuations in water near hydrophobic solutes: identifying the underlying physics
• Dimensionality reduction of local structure in glassy binary mixtures
• Nonequilibrium phase behaviour from minimization of free power dissipation
• Flow and structure in nonequilibrium Brownian many-body systems
• Modeling diffusion in colloidal suspensions by dynamical density functional theory using fundamental measure theory of hard spheres
• Dynamical density functional theory for dense suspensions of colloidal hard spheres
• Controlling the microstructure and phase behavior of confined soft colloids by active interaction switching
• Open Systems out of Equilibrium: Theory and Simulation
• Machine-learning effective many-body potentials for anisotropic particles using orientation-dependent symmetry functions
• Understanding the physics of hydrophobic solvation
• Dynamical density functional theory for the drying and stratification of binary colloidal dispersions
• Phase separation of active Brownian particles in two dimensions: Anything for a quiet life
• Force balance in thermal quantum many-body systems from Noether's theorem
• Comparative study of force-based classical density functional theory
• Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics
• Variational deep learning of equilibrium transition path ensembles
• Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals
• Classifying the age of a glass based on structural properties: A machine learning approach
• Custom Flow in Molecular Dynamics
• Reduced-variance orientational distribution functions from torque sampling
• Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale
• Shear and bulk acceleration viscosities in simple fluids
• Dynamic Decay and Superadiabatic Forces in the van Hove Dynamics of Bulk Hard Sphere Fluids
• Learning intermolecular forces at liquid-vapor interfaces

Cited by in corpus (21)

• A review of active matter reviews
• Neural functional theory for inhomogeneous fluids: Fundamentals and applications
• Why neural functionals suit statistical mechanics
• Physics-informed Bayesian inference of external potentials in classical density-functional theory
• Hyper-density functional theory of soft matter
• Hyperforce balance via thermal Noether invariance of any observable
• Neural density functionals: Local learning and pair-correlation matching
• Neural density functional theory of liquid-gas phase coexistence
• Neural force functional for non-equilibrium many-body colloidal systems
• Why hyperdensity functionals describe any equilibrium observable
• Local measures of fluctuations in inhomogeneous liquids: Statistical mechanics and illustrative applications
• Metadensity functional theory for classical fluids: Extracting the pair potential
• Noether invariance theory for the equilibrium force structure of soft matter
• Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes
• Learning the bulk and interfacial physics of liquid-liquid phase separation with neural density functionals
• Exploring the role of hydrodynamic interactions in spherically-confined drying colloidal suspensions
• Why gauge invariance applies to statistical mechanics
• Active crystallization from power functional theory
• Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
• Determining the chemical potential via universal density functional learning
• Metadensity functional learning for classical fluids: Regularizing with pair correlations