Universal criticality of entropy production in chemical reaction networks

TL;DR

This paper analyzes the critical behavior of entropy production in chemical reaction networks at macroscopic nonequilibrium transitions, revealing universal scaling laws and bounds.

Contribution

It provides a classification of entropy-production fluctuations at bifurcations in chemical networks using advanced mathematical tools, establishing universal bounds.

Findings

Derived generic exponents for entropy-production fluctuations at bifurcations.

Established a universal scaling inequality relating fluctuations and responses.

Showed that entropy-production fluctuations serve as a sharper probe of criticality.

Abstract

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.