  Chemically active droplets provide simple models for cell-like systems that
can grow and divide. Such active droplet systems are driven away from
thermodynamic equilibrium and turn over chemically, which corresponds to a
simple metabolism. We consider two scenarios of non-equilibrium driving. First,
droplets are driven via the system boundaries by external reservoirs that
supply nutrient and remove waste (boundary-driven). Second, droplets are driven
by a chemical energy provided by a fuel in the bulk (bulk-driven). For both
scenarios, we discuss the conservation of energy and matter as well as the
balance of entropy. We use conserved and non-conserved fields to analyze the
non-equilibrium steady states of active droplets. Using an effective droplet
model, we explore droplet stability and instabilities leading to droplet
division. Our work reveals that droplet division occurs quite generally in
active droplet systems. Our results suggest that life-like processes such as
metabolism and division can emerge in simple non-equilibrium systems that
combine the physics of phase separation and chemical reactions.
