The search for high entropy alloys: a high-throughput $\textit{ab-initio}$ approach.

While the ongoing search to discover new high-entropy systems is slowly expanding beyond metals, a rational and effective method for predicting "$\textit{in silico}$" the solid solution forming ability of multi-component systems remains yet to be developed. In this article, we propose a novel high-throughput approach for estimating the transition temperature of a solid solution: $\textit{ab-initio}$ energies are incorporated into a mean field statistical mechanical model where the relative entropy, Kullback-Leibler divergence, is the key order parameter following the evolution of disorder. The method is corroborated by Monte Carlo simulations and the results from the current most reliable data for binary, ternary, quaternary and quinary systems (96.6%; 90.7%; 100% and 100%, of correct solid solution predictions, respectively). By scanning through the many thousands of systems available in the $\small{\mathrm{AFLOW}}$ consortium repository, it is possible to predict a plethora of potential previously unknown quaternary and quinary solid solutions for future experimental validation.