Force density functional theory in- and out-of-equilibrium

Abstract

When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.

References in corpus (54)

• Dynamic Density Functional Theory of Fluids
• Dynamical density functional theory and its application to spinodal decomposition
• Depletion potential in hard-sphere mixtures: theory and applications
• Effective Interactions in Active Brownian Suspensions
• Effective forces in colloidal mixtures: from depletion attraction to accumulation repulsion
• Understanding depletion forces beyond entropy
• Power functional theory for Brownian dynamics
• Depletion potential in hard sphere fluids
• A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids
• Power functional theory for many-body dynamics
• Primitive Model Electrolytes in the Near and Far Field: Decay Lengths from DFT and Simulations
• Entropic torque
• Critical Drying of Liquids
• Quantifying density fluctuations in water at a hydrophobic surface: evidence for critical drying
• Enhanced wavelength-dependent surface tension of liquid-vapour interfaces
• Noether's Theorem in Statistical Mechanics
• Use the force! Reduced variance estimators for densities, radial distribution functions and local mobilities in molecular simulations
• Active Brownian particles at interfaces: An effective equilibrium approach
• Non-negative Interfacial Tension in Phase-Separated Active Brownian Particles
• Phase coexistence of active Brownian particles
• Molecular Density Functional Theory of Water describing Hydrophobicity at Short and Long Length Scales
• Scalar fundamental measure theory for hard spheres in three dimensions. Application to hydrophobic solvation
• Efficient molecular density functional theory using generalized spherical harmonics expansions
• Better than counting: Density profiles from force sampling
• Machine-learning free-energy functionals using density profiles from simulations
• Velocity gradient power functional for Brownian dynamics
• Deconstructing temperature gradients across fluid interfaces: the structural origin of the thermal resistance of liquid-vapor interfaces
• Mean-Field Theory of Inhomogeneous Fluids
• Nonequilibrium phase behaviour from minimization of free power dissipation
• Flow and structure in nonequilibrium Brownian many-body systems
• Driven colloidal suspensions in confinement and density functional theory: Microstructure and wall-slip
• Structural nonequilibrium forces in driven colloidal systems
• Displacement field and elastic constants in non-ideal crystals
• Pressure, surface tension and curvature in active systems: A touch of equilibrium
• Force Balance Approach for Advanced Approximations in Density Functional Theories
• Solvent fluctuations around solvophobic, solvophilic and patchy nanostructures and the accompanying solvent mediated interactions
• The Differential Capacitance as a probe for the electric double layer structure and the electrolyte bulk composition
• Exact Short Time Dynamics for Steeply Repulsive Potentials
• Fluctuation profiles in inhomogeneous fluids
• The contact theorem for charged fluids: from planar to curved geometries
• On the coarse-grained density and compressibility of non-ideal crystals: general theory and an application to cluster crystals
• Phase separation of active Brownian particles in two dimensions: Anything for a quiet life
• Fundamental measure theory of inhomogeneous two-body correlation functions
• Nonequilibrium phase transitions of sheared colloidal microphases: Results from dynamical density functional theory
• The Cassie-Wenzel transition of fluids on nanostructured substrates: Macroscopic force balance versus microscopic density-functional theory
• A reformulation of time-dependent Kohn-Sham theory in terms of the second time derivative of the density
• The direct correlation function of a crystalline solid
• Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics
• Bypassing the energy functional in density functional theory: Direct calculation of electronic energies from conditional probability densities
• Structure factor of thin films near continuous phase transitions
• Conditional probability density functional theory
• Shear and bulk acceleration viscosities in simple fluids
• Dynamic Decay and Superadiabatic Forces in the van Hove Dynamics of Bulk Hard Sphere Fluids
• Local pressure for confined systems

Cited by in corpus (22)

• Why Noether's Theorem applies to Statistical Mechanics
• Perspective: How to overcome dynamical density functional theory
• 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
• Variance of fluctuations from Noether invariance
• Comparative study of force-based classical density functional theory
• Gauge Invariance of Equilibrium Statistical Mechanics
• Neural density functionals: Local learning and pair-correlation matching
• Hyperforce balance via thermal Noether invariance of any observable
• First-principles superadiabatic theory for the dynamics of inhomogeneous fluids
• Why hyperdensity functionals describe any equilibrium observable
• Local measures of fluctuations in inhomogeneous liquids: Statistical mechanics and illustrative applications
• Noether invariance theory for the equilibrium force structure of soft matter
• Reduced-variance orientational distribution functions from torque sampling
• Why gauge invariance applies to statistical mechanics
• Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
• 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
• Routes to the density profile and structural inconsistency