Universal criticality of entropy production in chemical reaction networks

Stochastic thermodynamics gives universal relations for microscopic entropy production, yet its critical behavior at macroscopic nonequilibrium transitions remains unclassified. We study well-mixed reversible chemical reaction networks in the macroscopic-first limit, where transitions arise as local bifurcations of mass-action dynamics. Using linear-noise formulas, center-manifold normal forms, and Floquet theory, we obtain generic exponents for entropy-production fluctuations and responses at pitchfork, transcritical, saddle-node, and Hopf bifurcations. Beyond this low-order classification, a trajectory-space Cram\'{e}r-Rao type bound yields the universal scaling inequality $\alpha - 2\beta \geq 0$. Hence divergent responses require divergent fluctuations, but not conversely, making entropy-production fluctuations a sharper probe of nonequilibrium criticality.