Functional Inertia Index of Memory-Retaining Brain Dynamics: A Measure of Large-Scale Brain Adaptability

Human cognition is deeply contextual: a single moment can reawaken distant memories and emotions, shaping how we perceive and respond through the brain's retention of the past. This continuously reveals an inertial influence, long implicit in brain dynamics, that governs how brain states persist, shift, and reorganize over time. To render this organizing principle observable in neural data, we formalize an inertial state-space model that is agnostic to the observational modality. Applied to resting-state fMRI, we show that functional inertia organizes brain activity into recurrent dynamical regimes, defines a stable whole-brain constraint linked to cognition, and exhibits circuit-level distributions associated with clinical symptoms. In schizophrenia, departures from normative inertial organization emerge consistently across these levels and are mediated by a shared system-level inertial magnitude, resolving apparent contradictions between stability and volatility in brain dynamics reported in prior work. Together, these results position functional inertia as a unifying principle that reframes brain dynamics as history-constrained state evolution rather than transient fluctuations.