Power functional theory for many-body dynamics

Abstract

The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is often an essential step. Power functional theory provides a unique and microscopically sharp formulation of this concept. The approach is based on an exact one-body variational principle to describe the dynamics of both overdamped and inertial classical and quantum many-body systems. In equilibrium, density functional theory is recovered, and hence spatially inhomogeneous systems are described correctly. The dynamical theory operates on the level of time-dependent one-body correlation functions. Two- and higher-body correlation functions are accessible via the dynamical test particle limit and the nonequilibrium Ornstein-Zernike route. We describe the structure of this functional approach to many-body dynamics, including much background as well as applications to a broad range of dynamical situations, such as the van Hove function in liquids, flow in nonequilibrium steady states, motility-induced phase separation of active Brownian particles, lane formation in binary colloidal mixtures, and both steady and transient shear phenomena.

arXiv comment63 pages, 8 figures

References in corpus (125)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Active Particles in Complex and Crowded Environments
• Dynamic Density Functional Theory of Fluids
• Dynamical density functional theory and its application to spinodal decomposition
• A continuum theory of phase separation kinetics for active Brownian particles
• Effective Interactions in Active Brownian Suspensions
• The classical mechanics of non-conservative systems
• Time-dependent density-functional description of nuclear dynamics
• Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
• Classical dynamical density functional theory: from fundamentals to applications
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Mode-Coupling Theory of the Glass Transition: A Primer
• Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
• Negative interfacial tension in phase-separated active suspensions
• Layering and position-dependent diffusive dynamics of confined fluids
• Thermodynamics predicts how confinement modifies hard-sphere dynamics
• Non-equilibrium sedimentation of colloids on the particle scale
• Iterative Reconstruction of Memory Kernels
• Tension and stiffness of the hard sphere crystal-fluid interface
• The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics
• Nonlinear rheology of colloidal dispersions
• Event-Driven Brownian Dynamics for Hard Spheres
• Power functional theory for Brownian dynamics
• From Equilibrium to Steady State: The Transient Dynamics of Colloidal Liquids under Shear
• Molecular hydrodynamics from memory kernels
• Dynamical Density Functional Theory For Microswimmers
• Molecular Density Functional Theory of Water
• Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions
• Reentrance effect in the lane formation of driven colloids
• Oscillating Modes of Driven Colloids in Overdamped Systems
• Coarse-Grained Modelling Out of Equilibrium
• Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?
• Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections
• A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids
• Density functional theory for colloidal mixtures of hard platelets, rods, and spheres
• Phase diagrams of binary mixtures of patchy colloids with distinct numbers of patches: The network fluid regime
• Dynamics in inhomogeneous liquids and glasses via the test particle limit
• The Local Compressibility of Liquids near Non-Adsorbing Substrates: A Useful Measure of Solvophobicity and Hydrophobicity?
• Fluctuating motion in an active environment
• Phase separation and multibody effects in three-dimensional active Brownian particles
• Critical Drying of Liquids
• Quantifying density fluctuations in water at a hydrophobic surface: evidence for critical drying
• Density profiles of a colloidal liquid at a wall under shear flow
• Use the force! Reduced variance estimators for densities, radial distribution functions and local mobilities in molecular simulations
• Noether's Theorem in Statistical Mechanics
• Topological protection of multiparticle dissipative transport
• Non-negative Interfacial Tension in Phase-Separated Active Brownian Particles
• Phase coexistence of active Brownian particles
• Mean-field dynamical density functional theory
• Self diffusion of particles in complex fluids: temporary cages and permanent barriers
• Molecular Density Functional Theory of Water describing Hydrophobicity at Short and Long Length Scales
• Collective forces in scalar active matter
• Scalar fundamental measure theory for hard spheres in three dimensions. Application to hydrophobic solvation
• Better than counting: Density profiles from force sampling
• Study of a water-graphene capacitor with molecular density functional theory
• A classical density functional from machine learning and a convolutional neural network
• Drying and Wetting Transitions of a Lennard-Jones Fluid: Simulations and Density Functional Theory
• Superadiabatic forces in Brownian many-body dynamics
• Nonequilibrium Ornstein-Zernike relation for Brownian many-body dynamics
• Active-Particle Polarization Without Alignment Forces
• Machine-learning free-energy functionals using density profiles from simulations
• Analytical classical density functionals from an equation learning network
• Classical density functional theory, unconstrained crystallization, and polymorphic behavior
• A density functional theory for general hard-core lattice gases
• Floating nematic phase in colloidal platelet-sphere mixtures
• Velocity gradient power functional for Brownian dynamics
• First-Principles Constitutive Equation for Suspension Rheology
• Phase stacking diagram of colloidal mixtures under gravity
• Rosenfeld functional for non-additive hard spheres
• Density depletion and enhanced fluctuations in water near hydrophobic solutes: identifying the underlying physics
• Mean-Field Theory of Inhomogeneous Fluids
• Colloidal topological insulators
• Extended dynamical density functional theory for colloidal mixtures with temperature gradients
• Brownian asymmetric simple exclusion process
• Nonequilibrium phase behaviour from minimization of free power dissipation
• Systematically extending classical nucleation theory
• Computing bulk and shear viscosities from simulations of fluids with dissipative and stochastic interactions
• Flow and structure in nonequilibrium Brownian many-body systems
• Monolayers of hard rods on planar substrates: I. Equilibrium
• Force Balance Approach for Advanced Approximations in Density Functional Theories
• Structural nonequilibrium forces in driven colloidal systems
• Non-Equilibrium Uptake Kinetics of Molecular Cargo into Hollow Hydrogels Tuned by Electrosteric Interactions
• Adaptive Brownian Dynamics
• Solvent fluctuations around solvophobic, solvophilic and patchy nanostructures and the accompanying solvent mediated interactions
• Lane formation in a driven attractive fluid
• Active ideal sedimentation: Exact two-dimensional steady states
• Custom flow in overdamped Brownian Dynamics
• Microscopic theory of solvent mediated long range forces: influence of wetting
• Stochastic thermodynamics of fluctuating density fields: Non-equilibrium free energy differences under coarse-graining
• Dynamic correlations in Brownian many-body systems
• Hard spheres at a planar hard wall: Simulations and density functional theory
• Polarization-Density Patterns of Active Particles in Motility Gradients
• Explicitly stable Fundamental Measure Theory models for classical density functional theory
• Bulk dynamics of Brownian hard disks: Dynamical density functional theory versus experiments on two-dimensional colloidal hard spheres
• Morphometric approach to many-body correlations in hard spheres
• The phase behaviour and structure of a fluid confined between competing (solvophobic and solvophilic) walls
• Layering Transitions and Solvation Forces in an Asymmetrically Confined Fluid
• Fluctuation profiles in inhomogeneous fluids
• Phase separation of active Brownian particles in two dimensions: Anything for a quiet life
• Gravity-induced phase phenomena in plate-rod colloidal mixtures
• Fundamental measure theory of inhomogeneous two-body correlation functions
• Active interface polarization is a state function
• Particle Conservation in Dynamical Density Functional Theory
• Monolayers of hard rods on planar substrates: II. Growth
• A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density
• The role of sample height in the stacking diagram of colloidal mixtures under gravity
• Non-isothermal fluctuating hydrodynamics and Brownian motion
• Dynamical density functional theory analysis of the laning instability in sheared soft matter
• Statics and dynamics of inhomogeneous liquids via the internal-energy functional
• Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics
• Memory effects in the Fermi-Pasta-Ulam Model
• Relaxation dynamics in fluids of platelike colloidal particles
• Thermodynamic formalism and linear response theory for non-equilibrium steady states
• Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory
• Dynamic Pair Correlations and Superadiabatic Forces in a Dense Brownian Liquid
• Sedimentation stacking diagram of binary colloidal mixtures and bulk phases in the plane of chemical potentials
• Stress correlation function and linear response of Brownian particles
• Custom Flow in Molecular Dynamics
• Particle-conserving dynamics on the single-particle level
• Superadiabatic forces in the dynamics of the one-dimensional Gaussian core model
• Shear and bulk acceleration viscosities in simple fluids
• Density functional for ternary non-additive hard sphere mixtures
• Reconsidering Power Functional Theory
• Nonequilibrium steady states in fluids of platelike colloidal particles
• Local phase transitions in driven colloidal suspensions

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• Force density functional theory in- and out-of-equilibrium
• Noether-Constrained Correlations in Equilibrium Liquids
• Perspective: New directions in dynamical density functional theory
• Why neural functionals suit statistical mechanics
• Force balance in thermal quantum many-body systems from Noether's theorem
• Hyper-density functional theory of soft matter
• Comparative study of force-based classical density functional theory
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• Hyperforce balance via thermal Noether invariance of any observable
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• Understanding probability and irreversibility in the Mori-Zwanzig projection operator formalism
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• Local measures of fluctuations in inhomogeneous liquids: Statistical mechanics and illustrative applications
• Dynamic density functional theory for drying colloidal suspensions: Comparison of hard-sphere free-energy functionals
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• Inhomogeneous steady shear dynamics of a three-body colloidal gel former
• Exploring the role of hydrodynamic interactions in spherically-confined drying colloidal suspensions
• Fluid flow inside slit-shaped nanopores: the role of surface morphology at the molecular scale
• Dynamic Decay and Superadiabatic Forces in the van Hove Dynamics of Bulk Hard Sphere Fluids
• Why gauge invariance applies to statistical mechanics
• Solitary cluster waves in periodic potentials: Formation, propagation, and soliton-mediated particle transport
• Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
• Colloidal transport in twisted lattices of optical tweezers
• Active crystallization from power functional theory
• Superadiabatic dynamical density functional study of Brownian hard-spheres in time-dependent external potentials
• Nonequilibrium mixture dynamics: A model for mobilities and its consequences
• Metadensity functional learning for classical fluids: Regularizing with pair correlations
• Feedback-controlled solute transport through chemo-responsive polymer membranes
• Dynamic Density Functional Theory with Inertia and Background Flow
• Nonlinear Langevin functionals for a driven probe
• Single-file transport of binary hard-sphere mixtures through periodic potentials
• Nonequilibrium phase transition in single-file transport at high crowding
• Non-equilibrium (thermo)dynamics of colloids under mobile piston compression