Fig. 9: Model-based perturbation analysis.

A Entropy flow \({\sigma }_{t}^{{{{\rm{flow}}}}}\) of mouse 574078 in the active condition, computed after rescaling the fitted parameters as θ → βθ. The dashed line indicates β = 1. B Forward entropy flow, \({\sigma }_{t}^{{{{\rm{forward}}}}}\). C Backward entropy flow, \({\sigma }_{t}^{{{{\rm{backward}}}}}\). D Shuffle-subtracted entropy flow in the active condition, isolating the contribution of interactions beyond firing rate dynamics. Entropy flow driven by interactions peaks at β < 1. E Shuffle-subtracted entropy flow in the passive condition. F Comparison of shuffle-subtracted entropy flow between active and passive conditions across all mice, showing significantly higher values in the active condition (Wilcoxon test, p = 1.455 × 10−10). Shuffle-subtracted entropy flow is obtained over a low-gain range β ∈ [0.2, 1.0] and across all bins. Lines connect active (left) to passive (right) for each mouse.