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It has long been observed that Earth's atmosphere is uniquely far from its thermochemical equilibrium state in terms of its chemical composition. Studying this state of disequilibrium is important both for understanding the role that life plays in the Earth system, and for its potential role in the detection of life on exoplanets. Here we present a methodology for assessing the strength of the biogeochemical cycling processes that drive disequilibrium in planetary atmospheres. We apply it to the simultaneous presence of CH₄ and O₂ in Earth's atmosphere, which has long been suggested as a sign of life that could be detected remotely. Using a simplified model, we identify that the most important property to quantify is not the distance from equilibrium, but the power required to drive it. A weak driving force can maintain a high degree of disequilibrium if the residence times of the compounds involved are long; but if the disequilibrium is high and the kinetics fast, we can conclude that the disequilibrium must be driven by a substantial source of energy. Applying this to Earth's atmosphere, we show that the biotically generated portion of the power required to maintain the methane–oxygen disequilibrium is around 0.67 TW, although the uncertainty in this figure is about 10% due to uncertainty in the global CH₄ production. Compared to the chemical energy generated by the biota by photosynthesis, 0.67 TW represents only a very small fraction and, perhaps surprisingly, is of a comparable magnitude to abiotically driven geochemical processes at the Earth's surface. We discuss the implications of this new approach, both in terms of enhancing our understanding of the Earth system, and in terms of its impact on the possible detection of distant photosynthetic biospheres.