Nonlocal Electrostatic Field Theory from Microscopic Description
Soft Condensed Matter
2026-07-17 v1 Statistical Mechanics
Abstract
The study of electric fields in soft materials converges either to the study of point-like particles (local) in nonlinear theories or to the use of particles with finite sizes in nonlocal linear theories. In this work we start from the microscopic equations of motion and construct a unified mean field Fokker-Planck equation that describes the non-equilibrium electrostatics of nonlocal nonlinear systems. We obtain a generalized Poisson-Boltzmann equation for such systems as well as their electrostatic free energy expression. In the linear approximation we obtain an anisotropic susceptibility in an isotropic fluid which allows for local linear response inversion in electrostatics.
Cite
@article{arxiv.2607.16429,
title = {Nonlocal Electrostatic Field Theory from Microscopic Description},
author = {Varazdat Stepanyan and Yevgeni Sh. Mamasakhlisov and Armen E. Allahverdyan},
journal= {arXiv preprint arXiv:2607.16429},
year = {2026}
}