Equilibrium-like behavior in far-from-equilibrium chemical reaction networks

TL;DR

This paper investigates conditions under which far-from-equilibrium chemical reaction networks exhibit equilibrium-like Poisson distributions and fluctuation-dissipation relations, revealing topological features that enforce such behavior.

Contribution

It provides a nearly complete characterization of when nonequilibrium reaction networks display equilibrium-like statistical properties based on their topology.

Findings

Networks with specific topologies have Poisson steady-state distributions.

Driven systems obey an analog of the fluctuation-dissipation theorem.

Results are relevant to biological systems and nonequilibrium thermodynamics.

Abstract

In an equilibrium chemical reaction mixture, the number of molecules present obeys a Poisson distribution. We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain an essentially complete answer. In particular, we show that networks with certain topological features must have a Poisson distribution, whatever the reaction rates. Such driven systems also obey an analog of the fluctuation-dissipation theorem. Our results may be relevant to biological systems and to the larger question of how equilibrium concepts might apply to nonequilibrium systems.