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This paper investigates the emergence of open chemical reaction network (CRN) dynamics and thermodynamics from closed CRNs. They demonstrate that open-CRN behavior emerges asymptotically in closed CRNs when timescale separation (fast reactions act as exchange mechanisms) and abundance separation (some species act as chemostats) are present. The analysis reveals that stochastic dynamics and thermodynamic structures like local detailed balance and entropy production arise naturally from the underlying closed system, unifying the foundations of nonequilibrium thermodynamics of CRNs.
Chemostats, traditionally treated as external idealizations, can emerge as intrinsic thermodynamic structures within closed chemical reaction networks.
We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying closed CRNs? While open CRNs provide the standard framework to describe out-of-equilibrium chemical systems, real systems are finite and ultimately relax to equilibrium, leaving the status of this description conceptually unresolved. Here we show that open-CRN behavior arises as an asymptotic regime of closed CRNs when two minimal and physically transparent conditions are met: a time-scale separation, whereby fast reactions effectively act as exchange mechanisms, and an abundance separation, whereby a subset of species behaves as chemostats with diverging chemical capacity. In this regime, both the stochastic dynamics and the thermodynamic structure \ -- including local detailed balance, entropy production, and free-energy balance \ -- emerge to leading order from the underlying closed CRN. Our results apply to arbitrary stoichiometries. They show that chemostats need not be introduced as external idealizations, but instead arise as emergent thermodynamic structures within closed systems, providing a unified and physically grounded foundation for the nonequilibrium thermodynamics of CRNs.
