  It is shown that the dual to the linear programming problem that arises in
constraint-based models of metabolism can be given a thermodynamic
interpretation in which the shadow prices are chemical potential analogues, and
the objective is to minimise free energy consumption given a free energy drain
corresponding to growth. The interpretation is distinct from conventional
non-equilibrium thermodynamics, although it does satisfy a minimum entropy
production principle. It can be used to motivate extensions of constraint-based
modelling, for example to microbial ecosystems.
