📝 SummarXiv

Abstract

The principle of maximum entropy (MaxEnt) applies to the canonical ensemble related to the number of particles, known as the $\mathcal{N}$-ensemble. This concept pertains to physical domains (or basins) that are treated as open systems capable of transferring charge through the exchange of electrons. In this context, fractional occupation numbers of electrons indicate a net charge, represented as $\nu$. This principle outlines the convex expansion of the density matrix (DM), based on three distinct electronic states: the neutral state and two ionic edge states, each with a charge limit of $\pm q$. The coefficients of expansion and the charge transference fraction $\nu$, are crucial for understanding electron distribution. We express the quantities discussed as functions of the chemical potential derived from the statistical ensemble. Our analysis focuses on the donor and acceptor characteristics of different domains in relation to these parameters. The physical compatibility of the current equilibrium states of the system is discussed within this statistical framework and the electronegativity of the domains is inferred from the physical behavior of the associated populations.