Interplay between noise and higher-order interactions in the stochastic Kuramoto model: From enhancement to explosive transitions

The interplay between noise and higher-order interactions shapes collective dynamics in complex systems. While noise is traditionally regarded as a disordering force, this study demonstrates its dual role in the Kuramoto model with simplicial complexes. By extending the Ott-Antonsen reduction to the stochastic domain, a low-dimensional mean-field theory is developed, yielding an exact effective potential landscape. This framework reveals that common pairwise-interaction noise acts constructively, creating a concave potential correction that enhances synchronization and significantly expands the bistable region. In contrast, the impact of higher-order interaction noise is strictly gated by the pairwise coupling, creating a singularity at incoherence that either expands the bistable region or structurally protects the pure synchronized state. Furthermore, the mechanism of noise-induced explosive synchronization is quantified via mean first-passage time theory, identifying the transition as a timescale competition between barrier crossing and observation window. These findings provide a thermodynamic framework for understanding noise-controlled switching in higher-order networks, demonstrating how noise, by reshaping the effective potential, governs synchronization transitions and enables abrupt ordering under certain conditions.