  Understanding the emergent behavior of chemical reaction networks (CRNs) is a
fundamental aspect of biology and its origin from inanimate matter. A closed
CRN monotonically tends to thermal equilibrium, but when it is opened to
external reservoirs, a range of behaviors is possible, including transition to
a new equilibrium state, a non-equilibrium state, or indefinite growth. This
study shows that slowly driven CRNs are governed by the conserved quantities of
the closed system, which are generally far fewer in number than the species.
Considering both deterministic and stochastic dynamics, a universal slow
dynamics equation is derived with singular perturbation methods, and is shown
to be thermodynamically consistent. The slow dynamics is highly robust against
microscopic details of the network, which may be unknown in practical
situations. In particular, non-equilibrium states of realistic large CRNs can
be sought without knowledge of bulk reaction rates. The framework is
successfully tested against a suite of networks of increasing complexity and
argued to be relevant in the treatment of open CRNs as chemical machines.
