  Models of bacterial growth tend to be `irreversible', allowing for the number
of bacteria in a colony to increase but not to decrease. By contrast, models of
molecular self-assembly are usually `reversible', allowing for addition and
removal of particles to a structure. Such processes differ in a fundamental way
because only reversible processes possess an equilibrium. Here we show at
mean-field level that dynamic trajectories of reversible and irreversible
growth processes are similar in that both feel the influence of attractors, at
which growth proceeds without limit but the intensive properties of the system
are invariant. Attractors of both processes undergo nonequilibrium phase
transitions as model parameters are varied, suggesting a unified way of
describing reversible and irreversible growth. We also establish a connection
at mean-field level between an irreversible model of growth (the magnetic Eden
model) and the equilibrium Ising model, supporting the findings made by other
authors using numerical simulations.
