Abstract The possibility to identify subjects from their brain activity was met enthusiastically, as it bears the possibility to individualize brain analyses. However, the nature of the processes generating subject-specific features remains unknown, as the literature does not point to specific mechanisms. In particular, most of the current literature uses techniques that are based on the assumption of stationarity (e.g. Pearson’s correlation), which do not hypothesize any mechanisms, and crashes against a large body of literature showing the complex, highly non-linear nature of brain activity. In this paper, we hypothesize that intermittent moments when large, non-linear perturbations spread across the brain (defined as neuronal avalanches in the context of critical dynamics) are the ones that carry subject-specific information, and that contribute the most to identifiability. To test this hypothesis, we apply the recently-developed avalanche transition matrix (ATM) to source reconstructed magnetoencephalographic data, as to characterize subject-speficic fast dynamics. Then, we perform identifiability analysis based on the ATMs, and compared the performance to more classical ways of estimating large-scale connections (which assume stationareity). We demonstrate that selecting the moments and places where neuronal avalanches spread improves identifiability (p<0.0001, permutation testing), despite the fact that most ot the data (i.e. the linear part) are discarded. Our results show that the non-linear part of the brain signals carries most of the subject-specific information, shading light on the nature of the processes that underlie subject-identifiability. Borrowing from statistical mechanics, a solid branch of physics, we provide a principled way to link emergent large-scale personalized activations to non-observable, microscopic processes.