  We study the solutions of Von Neumann's expanding model with reversible
processes for an infinite reaction network. We show that, contrary to the
irreversible case, the solution space need not be convex in contracting phases
(i.e. phases where the concentrations of reagents necessarily decrease over
time). At optimality, this implies that, while multiple dynamical paths of
global contraction exist, optimal expansion is achieved by a unique time
evolution of reaction fluxes. This scenario is investigated in a statistical
mechanics framework by a replica symmetric theory. The transition from a
non-convex to a convex solution space, which turns out to be well described by
a phenomenological order parameter (the fraction of unused reversible
reactions) is analyzed numerically.
