Rapid Mixing of Glauber Dynamics for Monotone Systems via Entropic Independence

We study the mixing time of Glauber dynamics on monotone systems. For monotone systems satisfying the entropic independence condition, we prove a new mixing time comparison result for Glauber dynamics. For concrete applications, we obtain \(\tilde O(n)\) mixing time for the random cluster model induced by the ferromagnetic Ising model with consistently biased external fields, and \(\tilde O(n^2)\) mixing time for the bipartite hardcore model under the one-sided uniqueness condition, where \(n\) is the number of variables in corresponding models, improving the best known results in [Chen and Zhang, SODA’23] and [Chen, Liu, and Yin, FOCS’23], respectively.