Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics

We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of
<br /><br />elementary reactions. Their dynamics is described by deterministic rate equations with mass action
<br /><br />kinetics. Our most general framework considers open networks driven by time-dependent chemostats.
<br /><br />The energy and entropy balances are established and a nonequilibrium Gibbs free energy is introduced.
<br /><br />The difference between this latter and its equilibrium form represents the minimal work done by the
<br /><br />chemostats to bring the network to its nonequilibrium state. It is minimized in nondriven detailed-balanced
<br /><br />networks (i.e., networks that relax to equilibrium states) and has an interesting information-theoretic
<br /><br />interpretation. We further show that the entropy production of complex-balanced networks (i.e., networks
<br /><br />that relax to special kinds of nonequilibrium steady states) splits into two non-negative contributions: one
<br /><br />characterizing the dissipation of the nonequilibrium steady state and the other the transients due to
<br /><br />relaxation and driving. Our theory lays the path to study time-dependent energy and information
<br /><br />transduction in biochemical networks.