Cycle-free subsystem

In a chemical system with S steps and a maximum of Q linearly independent elementary reactions every set of Q steps whose reactions are linearly independent constitutes a cycle-free subsystem. It is apparent that, if R(Sj),..., R(sq) are linearly independent, then no cycle can be formed with the steps... 

It is also often taken for granted that many of the Earth s subsystems are exposed to free oxygen (O2), leading to a range of one-way reactions of reduced materials (such as organic carbon or metal sulfides) to an oxidized form. As pointed out many times in earlier chapters, the oxidation-reduction status of the planet is the consequence of the dynamic interactions of biogeochemical cycles. As is the case with the acid-base balances, there is considerable sensitivity to perturbations of "redox" conditions, sometimes dramatically as in the case of bodies of water that suddenly become anaerobic because of eutrophication. Another extreme... 

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