The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed . We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain a nearly 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 and can equilibrate when in contact with each other . Our results may be relevant to biological systems and to the larger question of how equilibrium ideas might extend to nonequilibrium systems.
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.
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