A first principles approach to electromechanics in liquids

Abstract: Electromechanics in fluids describes the response of the number density to electric fields, and thus provides a powerful means by which to control the behavior of liquids. While continuum approaches have proven successful in describing electromechanical phenomena in macroscopic bodies, their use is questionable when relevant length scales become comparable to a system's natural correlation lengths, as commonly occurs in, e.g., biological systems, nanopores, and microfluidics. Here, we present a first principles theory for electromechanical phenomena in fluids. Our approach is based on the recently proposed hyperdensity functional theory [Samm\"uller et al, Phys. Rev. Lett. 133, 098201 (2024)] in which we treat the charge density as an observable of the system, with the intrinsic Helmholtz free energy functional dependent upon both density and electrostatic potential. Expressions for the coupling between number and charge densities emerge naturally in this formalism, avoiding the need to construct density-dependent and spatially-varying material parameters such as the dielectric constant. Furthermore, we make our theory practical by deriving a connection between hyperdensity functional theory and local molecular field theory, which facilitates machine learning explicit representations for the free energy functionals of systems with short-ranged electrostatic interactions, with long-ranged effects accounted for in a well-controlled mean field fashion.