Emergence of Open Chemical Reaction Network Thermodynamics within Closed Systems

TL;DR

This paper demonstrates that open chemical reaction network thermodynamics can emerge from closed systems under specific conditions, unifying the understanding of equilibrium and nonequilibrium behaviors.

Contribution

It identifies minimal conditions under which closed CRNs exhibit open CRN thermodynamics, showing chemostats as emergent structures rather than external assumptions.

Findings

Open CRN behavior emerges as an asymptotic regime of closed CRNs.

Thermodynamic structures like entropy production emerge from closed systems.

Chemostats can arise intrinsically within closed systems under certain conditions.

Abstract

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.