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Abstract Neurophysiological measurements suggest that human information processing is evinced by neuronal activity. However, the quantitative relationship between the activity of a brain region and its information processing capacity remains unclear. We introduce and validate a mathematical model of the information processing capacity of a brain region in terms of neuronal activity, input storage capacity, and the arrival rate of afferent information. We applied the model to fMRI data obtained from a flanker paradigm in young and old subjects. Our analysis showed that—for a given cognitive task and subject—higher information processing capacity leads to lower neuronal activity and faster responses. Crucially, processing capacity—as estimated from fMRI data—predicted task and age-related differences in reaction times, speaking to the model’s predictive validity. This model offers a framework for modelling of brain dynamics in terms of information processing capacity, and may be exploited for studies of predictive coding and Bayes-optimal decision-making.