Ok so hopefully we now have some intuition that catalysis is the basis for non-equilibrium distributions of matter, and that the likelihood of catalyzing a particular transformation increases as molecular complexity increases. Complexity, in turn, is guaranteed to increase given a stable and sufficient input of energy and as-yet unexplored molecular possibilities. The final step in preparing the biosphere for the emergence of life is the formation of the first metabolic cycles.

In his 68 text, Morowitz provided a proof for the following theorem:

* In steady state systems, the flow of energy through the system from a source to a sink will lead to at least one cycle in the system.*

The proof is much too complicated to reproduce in this context, but we can understand the physical basis for this claim nevertheless. Let’s begin by returning to a materially closed system that can exchange light and heat with its surroundings but not mass. If this system is subjected to an energy gradient between a source and a sink, what are its available means of dissipating potential energy? First imagine a visible photon entering the system and being absorbed by an atom. This input energy will result in an electron being “promoted” to an excited state. The excited state has more potential energy than the ground state (the atom before absorbing the photon). This potential energy must dissipate* somehow*. The thing is, if the electron drops back to its ground state via exactly the reverse of the pathway that it took to get to the excited state, then the overall transformation is reversible and by definition this involves no dissipation (only irreversible processes produce entropy). In order for dissipation to occur the path to the high energy state must be different than path back to the lower energy state. But what I just described is a cycle. If you end up where you started via a different route than you left from, you have moved in a cycle. In order for energy to be dissipated by a materially closed system, at least one cycle must exist because this is simply the logically necessary condition for the perpetuation of an irreversible process in a closed system. As I’ve mentioned before, the biosphere as a whole is just such a materially closed system interposed between a stable energy gradient (sun and space). So this statement applies to the earth as a whole:* In order for energy to flow, matter must cycle.*