The principle of the circular economy is to reintroduce end-of-life materials back into the economic cycle. While reintroduction processes, for example, recycling or refurbishing, undoubtedly support this objective, they inevitably present material losses or generation of undesired by-products. Balancing losses and recoveries into a single and logical assessment has now become a major concern. The present work broadens the use of relative statistical entropy and material flow analysis to assess the recycling processes of two lithium-ion batteries previously published in the literature. Process simulation software, that is, HSC Sim®, was employed to evaluate with a high level of accuracy the performance of such recycling processes. Hereby, this methodology introduces an entropic association between the quality of final recoveries and the pre-processing stages, that is, shredding, grinding, and separation, by a parameter based on information theory. The results demonstrate that the pre-processing stages have a significant impact on the entropy value obtained at the final stages, reflecting the losses of materials into waste and side streams. In this manner, it is demonstrated how a pre-processing system capable of separating a wider number of components is advantageous, even when the final quality of refined products in two different processes is comparable. Additionally, it is possible to observe where the process becomes redundant, that is, where processing of material does not result in a significant concentration in order to take corrective actions on the process. The present work demonstrates how material flow analysis combined with statistical entropy can be used as a parameter upon which the performance of multiple recycling processes can be objectively compared from a material-centric perspective.