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We delve into growing open chemical reaction systems (CRSs) characterized byautocatalytic reactions within a variable volume, which changes in response tothese reactions. Understanding the thermodynamics of such systems is crucialfor comprehending biological cells and constructing protocells, as it shedslight on the physical conditions necessary for their self-replication. Buildingon our recent work, where we developed a thermodynamic theory for growing CRSsfeaturing basic autocatalytic motifs with regular stoichiometric matrices, wenow expand this theory to include scenarios where the stoichiometric matrix hasa nontrivial left kernel space. This extension introduces conservation laws,which limit the variations in chemical species due to reactions, therebyconfining the system's possible states to those compatible with its initialconditions. 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 theconserved quantities significantly influence the equilibrium state achieved bya growing CRS. These results are derived independently of specificthermodynamic potentials or reaction kinetics, therefore underscoring thefundamental impact of conservation laws on the growth of the system.

Thermodynamic and Stoichiometric Laws Ruling the Fates of Growing Systems