Mixing entropy and product recycling

Abstract

In this paper, we explore the relationship between the mixture of materials used in a product and the extent of end-of-life materials recycling from retired products in the United States. This is done for 14 common products, which are either widely recycled or not recycled. The results demonstrate the utility of using a normalized mixing entropy measure, identical to Shannon information, to resolve the products that are recycled and not recycled. The success of this measure is explained by outlining an analogy between recycling systems and communications theory. Two key observations are required: 1) the same axioms which establish Shannon information, "H", as a measure of the information content of a message, can also apply to a measure of mixing for materials, and 2) just as message codes can be represented as tree diagrams, so too can recycling systems. Using a well known communications theory result, Shannon's noiseless coding theorem, this analogy shows that "H" for material mixtures represents a reasonable lower bound on the cost of separation.