Imaginary Entropy in Human Eeg Traces

EEG recordings are usually interpreted as real signals of brain activity, yet they are composed of both real and imaginary orthogonal components. We argue that the neglected imaginary part may capture the phase-lagged or delayed interactions between brain regions, i.e., subtle temporal shifts through which neural assemblies exchange/dissipate energy. We propose here imaginary entropy ( ) as a quantitative index of time-lagged coupling diversity, derived from the Hilbert-transformed analytic representation of EEG signals. By normalizing the absolute imaginary amplitudes and calculating their Shannon entropy, could quantify how widely the brain’s dissipative interactions are spread across time and space, capturing the extent to which energy exchanges are concentrated or distributed within cortical activity. We showed that resting-state EEG recordings from healthy adults yielded consistent values with little variation across individuals. Comparisons with theoretical simulations including white, pink, and brown noise as well as damped oscillators demonstrated that empirical values align closely with those of pink-to-brown noise, i.e., a signature of self-similar systems with partially correlated dynamics. Grounding the analysis of brain activity in the physical concepts of complex response and energy dissipation traditionally linked to imaginary components, uncovers a hidden dimension of neural dynamics that reflects the balance between coherence and dissipation. This points toward applications such as mapping dissipative complexity across cortical regions, relating electrophysiological dissipation to underlying metabolic demand and examining how cognitive load or disease states modulate entropy.