Abstract
Carbon near the Earth's surface cycles between the production and consumption of organic carbon; the former sequesters carbon dioxide while the latter releases it. Microbes attempt to close the loop, but the longer organic matter survives, the slower microbial degradation becomes. This aging effect leaves observable quantitative signatures: Organic matter decays at rates that are inversely proportional to its age, while microbial populations and concentrations of organic carbon in ocean sediments decrease at distinct powers of age. Yet mechanisms that predict this collective organization remain unknown. Here, I show that these and other observations follow from the assumption that the decay of organic matter is limited by progressively rare extreme fluctuations in the energy available to microbes for decomposition. The theory successfully predicts not only observed scaling exponents but also a previously unobserved scaling regime that emerges when microbes subsist on the minimum energy flux required for survival. The resulting picture suggests that the carbon cycle's age-dependent dynamics are analogous to the slow approach to equilibrium in disordered systems. The impact of these slow dynamics is profound: They preclude complete oxidation of organic carbon in sediments, thereby freeing molecular oxygen to accumulate in the atmosphere.