Statistical entropy analysis as a proxy method for quantitative evaluation of phosphorus of a food-based bioethanol system

As an essential mineral element to sustain human existence, phosphorus (P) is a non-renewable resource and in food production, there is no substitute for it. Increasingly P resource stress and runoff pollution have inspired the search for more accurate and concise P management. In this study, mass joint entropy (MJE), an indicator that is based on statistical entropy, was introduced to describe the synergistic effect between P concentration and mass. Statistical entropy analysis (SEA) in combination with substance flow analysis (SFA) was used to qualify the P entropy trends. The life cycle of food-based (corn and cassava) bioethanol production in China served as the system for a case study to demonstrate this entropy-based method for quantitative P evaluation. Among the output, effluent from a fertilizer factory with the highest MJE for both corn (2.4 x 10(-4)) and cassava (6.5 x 10(-5)) contributed to the greatest amount of P emissions; wastewater sludge shows the strongest utilization potential for both. The SEA of the P life cycle reveals that the corn-based system, with a relative statistical entropy (RSE) of 0.28, is significantly more efficient in P utilization than the cassava-based system (RSE of 0.33), which is reinforced by the stronger link between organic fertilizer (livestock manure and by-products of ethanol production) to the arable land. Therefore, through combining SEA on the basis of SFA, the P system can be deeply understood from the perspectives of pollution and circulation, mass and information storage/transmission, status quo, and management. Such methodological advances will be crucial to evaluate the P resource utilization and pollution discharge in different processes and systems to fully embrace effective P management.

Automated summary

This study introduces mass joint entropy (MJE) and statistical entropy analysis (SEA) to evaluate the management and utilization of phosphorus resources, demonstrating this entropy-based quantitative evaluation method through a case study.