We build a rigorous nonequilibrium thermodynamic description for openchemical reaction networks of elementary reactions. Their dynamics is describedby deterministic rate equations satisfying mass action law. Our most generalframework considers open networks driven by time-dependent chemostats. Theenergy and entropy balances are established and a nonequilibrium Gibbs freeenergy is introduced. The difference between this latter and its equilibriumform represents the minimal work done by the chemostats to bring the network inits nonequilibrium state. It is minimized in nondriven detailed-balancednetworks (i.e. networks which relax to equilibrium states) and has aninteresting information-theoretic interpretation. We further show that theentropy production of complex balanced networks (i.e. networks which relax tospecial kinds of nonequilibrium steady states) splits into two non-negativecontributions. One charaterizing the dissipation of the nonequilibrium steadystate and the other the transients due to relaxation and driving. Our theorylays the path to study time-dependent energy and information transduction inbiochemical networks.
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