Kinetic and Thermodynamic Descriptions of Open Systems of Complex Chemical Reactions with Multiple Scales

Abstract

The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully appreciated outside the community of physical chemists. In this review, we discuss the latest advances in the kinetics and Gibbsian thermodynamics of chemical reactions in a spatially homogeneous aqueous solution with a multiscale perspective on complex systems. From the microscopic level of single reaction events which are purely stochastic in continuous time, one at a time among a set of molecules, to the macroscopic chemical reaction systems in bulk in terms of deterministic rate equations, the mathematical descriptions of kinetic models for chemical reactions at different levels are presented in detail, with rigorous mathematical justifications presented. In parallel with the kinetics of chemical reactions, the irreversible thermodynamics of open systems and the stochastic thermodynamics along reactions trajectories are reviewed thoroughly. As a novel feature, the mathematical theory of large deviations is shown to play a pivotal role in the thermodynamics of chemical reactions in equilibrium and in irreversible processes. This review is expected to stimulate interests in and help defining multiscale phenomena and nonequilibrium thermodynamics in many research fields on population dynamics of interacting species using chemical reactions as an analytic paradigm.