Electroencephalography (EEG) provides a non-invasive insight into the brain's cognitive and emotional dynamics. However, modeling how these states evolve in real time and quantifying the energy required for such transitions remains a major challenge. The Schrödinger Bridge Problem (SBP) offers a principled probabilistic framework to model the most efficient evolution between the brain states, interpreted as a measure of cognitive energy cost. While generative models such as GANs have been widely used to augment EEG data, it remains unclear whether synthetic EEG preserves the underlying dynamical structure required for transition-based analysis. In this work, we address this gap by using SBP-derived transport cost as a metric to evaluate whether GAN-generated EEG retains the distributional geometry necessary for energy-based modeling of cognitive state transitions. We compare transition energies derived from real and synthetic EEG collected during Stroop tasks and demonstrate strong agreement across group and participant-level analyses. These results indicate that synthetic EEG preserves the transition structure required for SBP-based modeling, enabling its use in data-efficient neuroadaptive systems. We further present a framework in which SBP-derived cognitive energy serves as a control signal for adaptive human-machine systems, supporting real-time adjustment of system behavior in response to user cognitive and affective state.

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