  We identify the thermodynamic conditions necessary to observe indefinite
growth in homogeneous open chemical reaction networks (CRNs) satisfying mass
action kinetics. We also characterize the thermodynamic efficiency of growth by
considering the fraction of the chemical work supplied from the surroundings
that is converted into CRN free energy. We find that indefinite growth cannot
arise in CRNs chemostatted by fixing the concentration of some species at
constant values, or in continuous-flow stirred tank reactors. Indefinite growth
requires a constant net influx from the surroundings of at least one species.
In this case, unimolecular CRNs always generate equilibrium linear growth,
i.e., a continuous linear accumulation of species with equilibrium
concentrations and efficiency one. Multimolecular CRNs are necessary to
generate nonequilibrium growth, i.e., the continuous accumulation of species
with nonequilibrium concentrations. Pseudo-unimolecular CRNs - a subclass of
multimolecular CRNs - always generate asymptotic linear growth with zero
efficiency. Our findings demonstrate the importance of the CRN topology and the
chemostatting procedure in determining the dynamics and thermodynamics of
growth.
