Odum–Tennenbaum–Brown calculus vs emergy and co-emergy analysis

•Linear algebra is not appropriate for emergy algebra.•Emergy co-emergy analysis does not give the same results as emergy algebra.•Emergy co-emergy assessment contains intrinsically a double-counting issue.•The mathematical structure of emergy algebra is an idempotent semi-ring.

In a recent paper Tennenbaum introduced a new method of calculating emergy that requires only ordinary (i.e. linear) algebra. We prove on a simple example with one feedback and one split that ordinary algebra as developed by Tennenbaum in his paper is not sufficient to tackle the problem of emergy analysis. In particular, we point out the problem of enumerating pathways which are relevant for emergy analysis, i.e. which avoid the double counting problem of feedbacks. Hence, the emergy co-emergy analysis cannot work at least for energy system diagram with splits and feedbacks. Le Corre and Truffet have already proved that the emergy path-finding problem deals with idempotent (thus non-linear) algebra.