On statistical entropy measures in material flow analysis and their common framework

Statistical entropy (SE) is a method to quantify distributions of any metric. In material flow analysis, SE was initially applied to examine the distribution of a single chemical element over a set of material flows. This made it possible to quantify the entropy change caused by a process with respect to a single substance. However, using Shannon's SE equation in another way, SE can also be applied to the distribution of all substances within one specific material flow. This paper presents how these two approaches are actually connected and how the first can be derived from the second in a mathematically sound, straightforward way. Finally, we show how to compute the combined SE for a set of material flows with respect to several selected substances.