  We delve into growing open chemical reaction systems (CRSs) characterized by
autocatalytic reactions within a variable volume, which changes in response to
these reactions. Understanding the thermodynamics of such systems is crucial
for comprehending biological cells and constructing protocells, as it sheds
light on the physical conditions necessary for their self-replication. Building
on our recent work, where we developed a thermodynamic theory for growing CRSs
featuring basic autocatalytic motifs with regular stoichiometric matrices, we
now expand this theory to include scenarios where the stoichiometric matrix has
a nontrivial left kernel space. This extension introduces conservation laws,
which limit the variations in chemical species due to reactions, thereby
confining the system's possible states to those compatible with its initial
conditions. By considering both thermodynamic and stoichiometric constraints,
we clarify the environmental and initial conditions that dictate the CRSs'
fate-whether they grow, shrink, or reach equilibrium. We also find that the
conserved quantities significantly influence the equilibrium state achieved by
a growing CRS. These results are derived independently of specific
thermodynamic potentials or reaction kinetics, therefore underscoring the
fundamental impact of conservation laws on the growth of the system.
