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

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.

5 pages, 2 figures; brief discussion of non-mass-action kinetics added

References in corpus (9)

• Effective Temperatures of a Driven System Near Jamming
• Stochastic fluctuations in metabolic pathways
• Experimental measurement of an effective temperature for jammed granular materials
• Effective Temperatures in Driven Systems: Static vs. Time-Dependent Relations
• Effective temperatures and activated dynamics for a two-dimensional air-driven granular system on two approaches to jamming
• Effective Temperatures in Athermal Systems Sheared at Fixed Normal Load
• Frequency-dependent fluctuation-dissipation relations in granular gases
• Fluctuation-dissipation relations in driven dissipative systems
• Temperature of a Hamiltonian system given as the effective temperature of a non-equilibrium steady state Langevin thermostat

Cited by in corpus (7)

• Topologically-constrained fluctuations and thermodynamics regulate nonequilibrium response
• Nonequilibrium Thermodynamics of Non-Ideal Reaction-Diffusion Systems: Implications for Active Self-Organization
• Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks
• Exchange of stability as a function of system size in a nonequilibrium system
• Diffusion-dynamics laws in stochastic reaction networks
• Insights into the relation between noise and biological complexity
• Physical limits on chemical sensing in bounded domains