Subject differentiation bears the possibility to individualize brain analyses. However, the nature of the processes generating subject-specific features remains unknown. Most of the current literature uses techniques that assume stationarity (e.g., Pearson’s correlation), which might fail to capture the non-linear nature of brain activity. We hypothesize that non-linear perturbations (defined as neuronal avalanches in the context of critical dynamics) spread across the brain and carry subject-specific information, contributing the most to differentiability. To test this hypothesis, we compute the avalanche transition matrix (ATM) from source-reconstructed magnetoencephalographic data, as to characterize subject-specific fast dynamics. We perform differentiability analysis based on the ATMs, and compare the performance to that obtained using Pearson’s correlation (which assumes stationarity). We demonstrate that selecting the moments and places where neuronal avalanches spread improves differentiation (P textless 0.0001, permutation testing), despite the fact that most of 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, thereby clarifying the nature of the processes that underlie individual differentiation. Borrowing from statistical mechanics, we provide a principled way to link emergent large-scale personalized activations to non-observable, microscopic processes.