Ergodic breakdown of brain dynamics under chronnectome complexity across cognitive states and age

Chronnectome complexity, the extent to which time-varying functional connectivity follows a structured sequence of distinct configurations, contributes to shaping large-scale brain dynamics. However, it remains unclear how this complexity influences the encoding of information that distinguishes resting state and task conditions. In ergodic theory, time averages represent ensemble behavior under ergodicity, which breaks down when dynamics are non-stationary, as when activity moves sequentially between distinct regimes. We hypothesize that this information resides in time-averaged connectivity under lower-complexity conditions but in trajectory geometry under higher-complexity conditions, where brain activity traverses distinct configurations over time, consistent with ergodic breakdown, which we term the \textit{information migration principle}. We formulate this as dynamics-driven multi-class classification and introduce the Brain Dynamics Classifier (BDC), an interpretable data-driven mechanistic model in which a graph neural network embeds dynamic functional connectivity into a latent space and a neural ordinary differential equation learns the vector field governing trajectories through that space. The proposed model derives two complementary representations within a single learned dynamical system, capturing time-averaged connectivity, which is sufficient under ergodic dynamics, and trajectory geometry, which preserves the temporal organization obscured by averaging under non-ergodic dynamics. Our results show high classification accuracy, $97.4\%$ for eight conditions in the Human Connectome Project young adult cohort and $92.2\%$ for four in the aging cohort. To test the information migration principle, we ablated the time-averaged representation and found that trajectory contributions varied with chronnectome complexity, from high for Working Memory to absent for Relational Reasoning, consistent with ergodic breakdown. Including subcortical regions further increased trajectory contributions for affective conditions. In aging, the distinction between higher and lower complexity conditions was preserved, resting-state dynamics became less ergodic with advancing age, and higher fluid intelligence was associated with more ergodic resting-state dynamics.