  Exploiting physical processes for fast and energy-efficient computation bears
great potential in the advancement of modern hardware components. This paper
explores non-linear charge tunneling in nanoparticle networks, controlled by
external voltages. The dynamics are described by a master equation, which
describes the development of a distribution function over the set of charge
occupation numbers. The driving force behind this evolution are charge
tunneling events among nanoparticles and their associated rates. In this paper,
we introduce two meanfield approximations to this master equation. By
parametrization of the distribution function using its first- and second-order
statistical moments, and a subsequent projection of the dynamics onto the
resulting moment manifold, one can deterministically calculate expected charges
and currents. Unlike a kinetic Monte Carlo approach, which extracts samples
from the distribution function, this meanfield approach avoids any random
elements. A comparison of results between the meanfield approximation and an
already available kinetic Monte Carlo simulation demonstrates great accuracy.
Our analysis also reveals that transitioning from a first-order to a
second-order approximation significantly enhances the accuracy. Furthermore, we
demonstrate the applicability of our approach to time-dependent simulations,
using eulerian time-integration schemes.
