The dynamic interplay between brain entropy and functional connectivity

• Dynamic BEN states co-vary with distinct whole-brain connectivity patterns and show different cognitive relevance. • Intermediate BEN states exhibit balanced integration–segregation, indicating that moderate BEN reflects higher neural complexity. • The cognitively beneficial BEN state showed low entropy and strong integration among the DMN, ECN, and SAN networks, highlighting the network basis of its positive cognitive profile. • BEN–FC coupling was state-dependent and strongest during this beneficial state, suggesting that such synchrony marks an optimal brain configuration. Brain entropy (BEN) quantifies the irregularity of regional brain activity and serves as an index of neural complexity, yet how BEN co-varies with large-scale brain connectivity remains unclear. Given the brain’s dynamic nature, this study examined how whole-brain connectivity patterns co-vary with recurring BEN states. Using a large resting-state fMRI data dataset (N = 812), we applied a sliding-window approach and k-means clustering to derive dynamic BEN states and their corresponding connectivity patterns. Four distinct BEN states were identified, each showing unique functional and cognitive relevance. A low-BEN state (State 1) was associated with a strongly segregated, weakly integrated organization and negative cognitive relevance, while a high-BEN state (State 4) showed a highly integrated but weakly segregated organization and neutral cognitive relevance. Two intermediate-BEN states differed in regional entropy and connectivity: State 2, with low entropy in the default mode (DMN), executive control (ECN), and salience (SAN) networks, showed positive cognitive relevance and balanced integration–segregation; State 3, with low entropy in sensorimotor (SMN) and visual networks (VN), showed no significant cognitive relevance. Moreover, BEN–connectivity correlations were significantly negative and varied across states, being strongest in the cognitively relevant states. These findings demonstrate that the relationship between BEN and brain connectivity is dynamic and state-dependent, advancing BEN as a marker of the brain’s complex, state-dependent functional organization.