Hyper-density functional theory of soft matter

Abstract

We present a scheme for investigating arbitrary thermal observables in spatially inhomogeneous equilibrium many-body systems. Extending the grand canonical ensemble yields any given observable as an explicit hyper-density functional. Associated local fluctuation profiles follow from an exact hyper-Ornstein-Zernike equation. While the local compressibility and simple observables permit analytic treatment, complex order parameters are accessible via simulation-based supervised machine learning of neural hyper-direct correlation functionals. We exemplify efficient and accurate neural predictions for the cluster statistics of hard rods, square well rods, and hard spheres. The theory allows to treat complex observables, as is impossible in standard density functional theory.

7 pages, 2 figures + supplementary material (4 pages, 1 figure)

References in corpus (41)

• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Deep-Learning Density Functional Theory Hamiltonian for Efficient ab initio Electronic-Structure Calculation
• Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
• Machine learning and density functional theory
• Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory
• Computer simulation of fluid phase transitions
• Unsupervised learning for local structure detection in colloidal systems
• Molecular Density Functional Theory of Water
• Power functional theory for many-body dynamics
• A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids
• Neural-network Kohn-Sham exchange-correlation potential and its out-of-training transferability
• Primitive Model Electrolytes in the Near and Far Field: Decay Lengths from DFT and Simulations
• The Local Compressibility of Liquids near Non-Adsorbing Substrates: A Useful Measure of Solvophobicity and Hydrophobicity?
• Revealing the three-dimensional structure of liquids using four-point correlation functions
• Noether's Theorem in Statistical Mechanics
• Neural functional theory for inhomogeneous fluids: Fundamentals and applications
• 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
• Modified Poisson-Boltzmann equations and macroscopic forces in inhomogeneous ionic fluids
• A classical density functional from machine learning and a convolutional neural network
• Machine-learning free-energy functionals using density profiles from simulations
• Analytical classical density functionals from an equation learning network
• Thermodynamic entropy as a Noether invariant
• Machine learning many-body potentials for colloidal systems
• Density depletion and enhanced fluctuations in water near hydrophobic solutes: identifying the underlying physics
• Why Noether's Theorem applies to Statistical Mechanics
• Machine learning the derivative discontinuity of density-functional theory
• Perspective: How to overcome dynamical density functional theory
• Force density functional theory in- and out-of-equilibrium
• Machine-learning effective many-body potentials for anisotropic particles using orientation-dependent symmetry functions
• Physics-constrained Bayesian inference of state functions in classical density-functional theory
• Understanding the physics of hydrophobic solvation
• Fluctuation profiles in inhomogeneous fluids
• Reliable emulation of complex functionals by active learning with error control
• Noether's second theorem and covariant field theory of mechanical stresses in inhomogeneous ionic liquids
• Why neural functionals suit statistical mechanics
• Physics-informed Bayesian inference of external potentials in classical density-functional theory
• Thermodynamical path integral and emergent symmetry
• Hyperforce balance via thermal Noether invariance of any observable
• Local measures of fluctuations in inhomogeneous liquids: Statistical mechanics and illustrative applications
• Inhomogeneous steady shear dynamics of a three-body colloidal gel former

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• Why gauge invariance applies to statistical mechanics
• Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
• Dielectrocapillarity for exquisite control of fluids
• Determining the chemical potential via universal density functional learning
• The roles of bulk and surface thermodynamics in the selective adsorption of a confined azeotropic mixture
• Metadensity functional learning for classical fluids: Regularizing with pair correlations
• A unified machine-learning framework for ab initio multiscale modeling of liquids