  Within a fully microscopic setting, we derive a variational principle for the
non-equilibrium steady states of chemical reaction networks, valid for
time-scales over which chemical potentials can be taken to be slowly varying:
at stationarity the system minimizes a global function of the reaction fluxes
with the form of a Hopfield Hamiltonian with Hebbian couplings, that is
explicitly seen to correspond to the rate of decay of entropy production over
time. Guided by this analogy, we show that reaction networks can be formally
re-cast as systems of interacting reactions that optimize the use of the
available compounds by competing for substrates, akin to agents competing for a
limited resource in an optimal allocation problem. As an illustration, we
analyze the scenario that emerges in two simple cases: that of toy (random)
reaction networks and that of a metabolic network model of the human red blood
cell.
