Abstract
We formulate a nonequilibrium thermodynamic description for open chemical reaction networks (CRNs) described by a chemical master equation. The topological properties of the CRN and its conservation laws are shown to play a crucial role. They are used to decompose the entropy production into a potential change and two work contributions, the first due to time dependent changes in the externally controlled chemostats concentrations and the second due to flows maintained across the system by nonconservative forces. These two works jointly satisfy a Jarzynski and Crooks fluctuation theorem. In the absence of work, the potential is minimized by the dynamics as the system relaxes to equilibrium and its equilibrium value coincides with the maximum entropy principle. A generalized Landauer's principle also holds: the minimal work needed to create a nonequilibrium state is the relative entropy of that state to its equilibrium value reached in the absence of any work.
Highlights
Nonequilibrium thermodynamic descriptions of stochasticchemical processes have long since been developed
In particular, the stochastic description in terms of the Chemical Master Equation (CME)3,4 of nonlinear chemical reaction networks, i.e., CRNs described at the deterministic level by nonlinear rate equations for concentrations
We presented a thorough description of nonequilibrium thermodynamics of stochastic CRNs
Summary
Nonequilibrium thermodynamic descriptions of stochastic (bio-)chemical processes have long since been developed. Hill and co-workers studied bio-catalysts as small fluctuating machines operating at steady-state They introduced the concept of free energy transduction and analyzed how one form of chemical work can drive another one against its spontaneous direction.. They model, for instance, conformational changes of an enzyme or of a membrane transporter Inspired by these seminal studies, Schnakenberg formulated steady-state thermodynamics for generic Markov jump processes and provided a systematic cycle decomposition for the entropy production (EP) rate.. Inspired by these seminal studies, Schnakenberg formulated steady-state thermodynamics for generic Markov jump processes and provided a systematic cycle decomposition for the entropy production (EP) rate.2 He considered, in particular, the stochastic description in terms of the Chemical Master Equation (CME) of nonlinear chemical reaction networks, i.e., CRNs described at the deterministic level by nonlinear rate equations for concentrations. We derive a nonequilibrium Landauer’s principle for the driving and nonconservative work which generalizes the previous ones to nondetailed-balanced dynamics.
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