  High entropy alloys present a new class of disordered metals which hold
promising prospects for the next generation of materials and technology.
However, much of the basic physics underlying these robust, multifunctional
materials -- and those of other, more generic forms of disordered matter --
still remain the subject of ongoing inquiry. We thus present a minimal-working
model that describes the disorder-driven fluctuations in the electronic charge
distributions and electrostatic "Madelung" fields in disordered metals. Our
theory follows a standard perturbative scheme and captures the leading
contributions from dominant electronic processes, including electrostatic
screening and impurity scattering events. We show here that a modest
first-order treatment incorporating these effects is sufficient to reproduce
the linear charge transfer trends featured in both high-entropy and other
conventional alloys, our model also shedding light on the microscopic origins
of these statistical features. We further elaborate on the nature of these
electronic charge and Madelung field fluctuations by determining how these
emerge from the statistics of the underlying disorder, and how these can be
described using the linear response formulation that we develop here. In doing
so, our work answers various questions which have long-perplexed the disordered
materials community. It also opens up possible avenues for providing systematic
corrections to modern first-principles approaches to disorder-modeling (e.g.
the conventional CPA method) which currently lack these statistical features.
