Dynamic criticality - the balance between order and chaos - is fundamental in genome regulation and cellular transitions. In this study, we investigate the distinct behaviors of gene expression dynamics in MCF-7 breast cancer cells under two stimuli: Heregulin (HRG), which promotes cell fate transitions, and Epidermal Growth Factor (EGF), which, despite binding to the same receptor, does not induce cell fate changes. We model the system as an open, non-equilibrium thermodynamic system and introduce a convergence-based approach for the robust estimation of thermodynamic metrics.Our analysis reveals that the Shannon entropy of the critical point (CP) dynamically synchronizes with the entropy of the rest of the whole expression system (WES), reflecting coordinated transitions between ordered and disordered phases. This phase synchronization is driven by net mutual information scaling with CP entropy dynamics, demonstrating how the CP governs genome-wide coherence. Notably, high-order (multivariate) mutual information emerges as a defining feature of the synergistic network underlying gene expression regulation.By achieving thermodynamic phase synchronization, the CP orchestrates the entire expression system. Under HRG stimulation, the CP becomes active, functioning as a Maxwell’s demon with dynamic, rewritable chromatin memory to guide a critical transition in cell fate. In contrast, during EGF stimulation, the CP remains inactive in this strategic role, acting passively to facilitate non- critical transition.These findings, building on previous studies and our investigations, provide a biophysical framework for understanding thermodynamic synchronization in genomic expression, offering new strategies for cancer research and stem cell therapy.
