Resource efficiency from a statistical entropy perspective: Case study on phosphorus use in Austria

The turnover of materials of an economy has been described as the consumption of raw materials (low-entropy materials) that are used and transformed into products and wastes (high entropy materials). Thus, the economy can be... [ view full abstract ]

The turnover of materials of an economy has been described as the consumption of raw materials (low-entropy materials) that are used and transformed into products and wastes (high entropy materials). Thus, the economy can be viewed as an entropy-producing process. In a circular economy, entropy generation must be kept low. Generated wastes should be transformed into low-entropy recycled products that can reduce the use of primary resources. Entropy reduction is achieved by the concentration of materials or by avoiding dilution and dissipation. Hence, efficient resource use, from an entropy point of view, aims at minimizing the dilution of a substance during its use. The ability of a material flow system to concentrate or dilute a substance can be assessed by statistical entropy analysis (SEA).

The goal of the present study is to use SEA to evaluate the resource efficiency of a complex material flow system exemplified by phosphorus use in Austria. Contrary, to existing SEA applications on the macro-level, the Austrian P resource system is analyzed at a high level of detail, accounting for the interaction with foreign markets (import/export flows), various P recycling loops throughout the P lifecycle, and P stock dynamics. The efficiency of P use in Austria is evaluated from two perspectives: Firstly, P utilization is assessed for two different years (2000 vs. 2010) to explore the ability of SEA to reflect changes in P resource use over time. Secondly, optimized P management on the national level is assessed by applying SEA to a desired state of the system (=target system), which could be achieved by implementing specific measures aimed at reducing consumption, increasing recycling, and lowering emissions. For every life cycle stage of P in Austria a defined set of material flows is considered to calculate the relative statistical entropy (RSE) of the respective stage. Information on the P flow and the P concentration in the goods are extracted primarily from existing MFA studies for Austria, where relevant P flows have been balanced. All the P flows are defined as normally distributed variables and the uncertainty of the P flow estimates is consequently propagated through the statistical entropy computations. The evaluation results show the trend of statistical entropy across different lifecycle stages of P use in Austria for different states of the system (i.e. different years or target system). In all the cases, the RSE of P use increases from crop farming to the end-of-life phase. However, there are distinct differences in the evolution of RSE between the years 2000 and 2010 as well as with respect to the (idealized) target system. The latter exhibits a nearly horizontal RSE trend, which indicates that P dissipation is minimized and P is recovered at a very high rate from various residues in this system state. The results show, that the entropy approach improves our understanding of industrial metabolism and is a useful decision support and design tool, since the resource efficiency of complex systems can thereby be characterized by a single metric per resource.