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Partial equilibrium approximation (PEA) and quasi-steady-state approximation(QSSA) are two classical methods for reducing complex macroscopic chemicalreactions into simple computable ones. Previous studies mainly focus on theaccuracy of solutions before and after applying model reduction. While, in thispaper we start from a thermodynamic view, and try to establish a quantitativeconnection on the essential thermodynamic quantities, like entropy productionrate, free energy dissipation rate and entropy flow rate, between the originalreversible chemical mass-action equations and the reduced models by either PEAor QSSA. Our results reveal that the PEA and QSSA do not necessarily preservethe nice thermodynamic structure of the original full model during thereduction procedure (e.g. the loss of non-negativity of free energy dissipationrate), especially when adopting the algebraic relations in replace ofdifferential equations. These results are further validated though theapplication to Michaelis-Menten reactions analytically and numerically as aprototype. We expect our study would motivate a re-examination on theeffectiveness of various model reduction or approximation methods from a newperspective of non-equilibrium thermodynamics.

Thermodynamics for Reduced Models of Chemical Reactions by PEA and QSSA