  The purpose of this work is to clarify how the stoichiometric trait of
autocatalytic networks, namely their absence of a conservation law, shapes
their non-equilibrium behavior. To do so, we consider an autocatalytic network
coupled with external species acting as food/waste materials, necessary to
fulfill mass conservation. Then, we show that the production of autocatalytic
species requires a conservative influx of these external species. From this, we
derive the thermodynamic potential of an autocatalytic sub-network. The latter
can be obtained from the usual semigrand free-energy of an open system by
taking into account the conservative work associated to the influx of external
species fueling the production of autocatalytic species. In the end, we
identify the cost dedicated to the production of autocatalytic species and its
efficiency. It reveals that sustaining steady production of species in an
autocatalytic network is possible only if they are coupled with the
environment.
