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Our planet is a self-sustaining ecosystem powered by light energy from the sun, but roughly closed to matter. Many ecosystems on Earth are also approximately closed to matter and recycle nutrients by self-organizing stable nutrient cycles, e.g., microbial mats, lakes, open ocean gyres. However, existing ecological models do not exhibit the self-organization and dynamical stability widely observed in such planetary-scale ecosystems. Here, we advance a conceptual model that explains the self-organization, stability, and emergent features of closed microbial ecosystems. Our model incorporates the bioenergetics of metabolism into an ecological framework. By studying this model, we uncover a crucial thermodynamic feedback loop that enables metabolically diverse communities to almost always stabilize nutrient cycles. Surprisingly, highly diverse communities self-organize to extract $\approx$10 $\%$of the maximum extractable energy, or $\approx$100 fold more than randomized communities. Further, with increasing diversity, distinct ecosystems show strongly correlated fluxes through nutrient cycles. However, as the driving force from light increases, the fluxes of nutrient cycles become more variable and species-dependent. Our results highlight that self-organization promotes the efficiency and stability of complex ecosystems at extracting energy from the environment, even in the absence of any centralized coordination.