  Our planet is roughly closed to matter, but open to energy input from the
sun. However, to harness this energy, organisms must transform matter from one
chemical (redox) state to another. For example, photosynthetic organisms can
capture light energy by carrying out a pair of electron donor and acceptor
transformations (e.g., water to oxygen, CO$_2$ to organic carbon). Closure of
ecosystems to matter requires that all such transformations are ultimately
balanced, i.e., other organisms must carry out corresponding reverse
transformations, resulting in cycles that are coupled to each other. A
sustainable closed ecosystem thus requires self-organized cycles of matter, in
which every transformation has sufficient thermodynamic favorability to
maintain an adequate number of organisms carrying out that process. Here, we
propose a new conceptual model that explains the self-organization and emergent
features of closed ecosystems. We study this model with varying levels of
metabolic diversity and energy input, finding that several thermodynamic
features converge across ecosystems. Specifically, irrespective of their
species composition, large and metabolically diverse communities self-organize
to extract roughly 10% of the maximum extractable energy, or 100 fold more than
randomized communities. Moreover, distinct communities implement energy
extraction in convergent ways, as indicated by strongly correlated fluxes
through nutrient cycles. As the driving force from light increases, however,
these features -- fluxes and total energy extraction -- become more variable
across communities, indicating that energy limitation imposes tight
thermodynamic constraints on collective metabolism.
