  Partial equilibrium approximation (PEA) and quasi-steady-state approximation
(QSSA) are two classical methods for reducing complex macroscopic chemical
reactions into simple computable ones. Previous studies mainly focus on the
accuracy of solutions before and after applying model reduction. While, in this
paper we start from a thermodynamic view, and try to establish a quantitative
connection on the essential thermodynamic quantities, like entropy production
rate, free energy dissipation rate and entropy flow rate, between the original
reversible chemical mass-action equations and the reduced models by either PEA
or QSSA. Our results reveal that the PEA and QSSA do not necessarily preserve
the nice thermodynamic structure of the original full model during the
reduction procedure (e.g. the loss of non-negativity of free energy dissipation
rate), especially when adopting the algebraic relations in replace of
differential equations. These results are further validated though the
application to Michaelis-Menten reactions analytically and numerically as a
prototype. We expect our study would motivate a re-examination on the
effectiveness of various model reduction or approximation methods from a new
perspective of non-equilibrium thermodynamics.
