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Accurate and efficient theoretical techniques for describing ionic fluids are highly desirable for many applications across the physical, biological and materials sciences. With a rigorous statistical mechanical foundation, classical density functional theory (cDFT) is an appealing approach, but the competition between strong Coulombic interactions and steric repulsion limits the accuracy of current approximate functionals. Here, we extend a recently presented machine learning (ML) approach [Samm\"uller et al., Proc. Natl. Acad. Sci. USA, 120, e2312484120 (2023)] designed for systems with short-ranged interactions to ionic fluids. By adopting ideas from local molecular field theory, the framework we present amounts to using neural networks to learn the local relationship between the one-body direct correlation functions and inhomogeneous density profiles for a "mimic'' short-ranged system, with effects of long-ranged interactions accounted for in a mean-field, yet well-controlled, manner. By comparing to results from molecular simulations, we show that our approach accurately describes the structure and thermodynamics of the prototypical model for electrolyte solutions and ionic liquids: the restricted primitive model. The framework we present acts as an important step toward extending ML approaches for cDFT to systems with accurate interatomic potentials., Comment: Main: 7 pages, 3 figures. SI: 16 pages, 8 figures

A central aim of statistical mechanics is to establish connections between a system's microscopic fluctuations and its macroscopic response to a perturbation. For non-equilibrium transport properties, this amounts to establishing Green-Kubo (GK) relationships. In hydrodynamics, relating such GK expressions for liquid-solid friction to macroscopic slip boundary conditions has remained a long-standing problem due to two challenges: (i) The GK running integral of the force autocorrelation function decays to zero rather than reaching a well-defined plateau value; and (ii) debates persist on whether such a transport coefficient measures an intrinsic interfacial friction or an effective friction in the system. Inspired by ideas from the coarse-graining community, we derive a GK relation for liquid-solid friction where the force autocorrelation is sampled with a constraint of momentum conservation in the liquid. Our expression does not suffer from the "plateau problem" and unambiguously measures an effective friction coefficient, in an analogous manner to Stokes' law. We further establish a link between the derived friction coefficient and the hydrodynamic slip length, enabling a straightforward assessment of continuum hydrodynamics across length scales. We find that continuum hydrodynamics describes the simulation results quantitatively for confinement length scales all the way down to 1 nm. Our approach amounts to a straightforward modification to the present standard method of quantifying interfacial friction from molecular simulations, making possible a sensible comparison between surfaces of vastly different slippage., Comment: Main: 12 pages, 3 figures. SI: 26 pages, 11 figures

A central aim of multiscale modeling is to use results from the Schr\"odinger Equation to predict phenomenology on length scales that far exceed those of typical molecular correlations. In this work, we present a new approach rooted in classical density functional theory (cDFT) that allows us to accurately describe the solvation of apolar solutes across length scales. Our approach builds on the Lum-Chandler-Weeks (LCW) theory of hydrophobicity [K. Lum et al., J. Phys. Chem. B 103, 4570 (1999)] by constructing a free energy functional that uses a slowly-varying component of the density field as a reference. From a practical viewpoint, the theory we present is numerically simpler and generalizes to solutes with soft-core repulsion more easily than LCW theory. Furthermore, by assessing the local compressibility and its critical scaling behavior, we demonstrate that our LCW-style cDFT approach contains the physics of critical drying, which has been emphasized as an essential aspect of hydrophobicity by recent theories. As our approach is parameterized on the two-body direct correlation function of the uniform fluid and the liquid-vapor surface tension, it straightforwardly captures the temperature dependence of solvation. Moreover, we use our theory to describe solvation at a first-principles level, on length scales that vastly exceed what is accessible to molecular simulations., Comment: Main: 11 pages, 4 figures. SI: 27 pages, 13 figures