Quantum-Like Representation of Dynamic Functional Connectivity: Double Covariance Formalism

We introduce a neurophysiological adaptation of the Double Covariance Model (DCM) to provide a generative, fourth-order statistical framework for brain dynamics. Moving beyond descriptive sliding-window methods, the proposed theory implements a two-scale temporal scheme that explicitly separates fast micro-time stochastic neural fluctuations from the macro-time scale of emergent cognitive states. By treating the variance of covariance as a first-class mathematical object, the model computes the fourth-order moment of localized micro-signals to directly reconstruct a complex-valued network density matrix ($\rho$). This architecture transitions classical neurophysiological data into a quantum-like state representation, enabling the direct application of quantum information measures—such as concurrence and von Neumann entropy—to model macroscopic integration. Ultimately, this framework establishes a principled, non-phenomenological link between low-level stochastic network dynamics and the unified macroscopic phenomenon of "mental entanglement".