Resolving the Entropy Paradox: Simulation-Validated Spectral Entropy Detects Fold Bifurcations in Preparation for Neural Measurement

Entropy paradox: how can cognitive processing be both highly dissipative on average and locally efficient during transitions?Here we propose a resolution grounded in temporal scale separation and provide the first simulation-validated measurement pipeline ready for human EEG testing. We distinguish clearly between (a) state entropy H(t), capturing the dispersion of neural activity across frequencies, and (b) information dissipation rate ID(t) = -dH/dt, quantifying the rate of entropy change. We demonstrate that fold bifurcations in a cubic gradient dynamical system (ẋ = r + x - x³) produce robust, measurable signatures: transient local minima in spectral entropy precisely at fold moments, detectable even under substantial noise contamination.Using Welch’s method for power spectral density estimation, we compute spectral entropy in 150-sample sliding windows, directly paralleling typical EEG analysis parameters (150ms windows at 1kHz sampling). Across four noise levels (σ = 0.05, 0.08, 0.10, 0.15) and 10 independent runs per condition, the pipeline detects entropy minima in 70-80% of simulations at three biologically plausible noise regimes, with medium to large effect sizes (Cohen’s d = 0.46-0.58, 95% CIs spanning 0.12-0.90). Only extreme noise (σ = 0.15) falls below criterion (50% detection), though effect sizes remain large when detected (d = 0.72). This satisfies our pre-specified validation criterion: ≥60% detection in ≥3/4 noise levels with d ≥ 0.40, establishing that the pipeline reliably detects fold-transition signatures in systems where ground truth is known.