  We provide a rigorous definition of free-energy transduction and its
efficiency in arbitrary -- linear or nonlinear -- open chemical reaction
networks (CRNs) operating at steady state. Our method is based on the knowledge
of the stoichiometric matrix and of the chemostatted species (i.e. the species
maintained at constant concentration by the environment) to identify the
fundamental currents and forces contributing to the entropy production.
Transduction occurs when the current of a stoichiometrically balanced process
is driven against its spontaneous direction (set by its force) thanks to other
processes flowing along their spontaneous direction. In these regimes, open
CRNs operate as thermodynamic machines. After exemplifying these general ideas
using toy models, we analyze central energy metabolism. We relate the
fundamental currents to metabolic pathways and discuss the efficiency with
which they are able to transduce free energy.
