Reaction-diffusion processes play an important role in a variety of physical, chemical, and biological systems. Conventionally, the kinetics of these processes are described by the law of mass action. However, there are various cases where these equations are insufficient. A fundamental challenge lies in accurately accounting for the microscopic correlations that inevitably arise in bimolecular reactions. While approaches to describe microscopic correlations in many specific cases exist, no general theory for multistage reactions has been established. In this article, we apply the quantum field theory approach to derive kinetic equations for general multistage reactive systems termed complete modified encounter theory (CMET). CMET can be formulated as a set of coupled partial differential equations that can be easily integrated numerically, thereby serving as a versatile tool for investigating reaction-diffusion processes. Across multiple case studies, we demonstrated that CMET reproduces the kinetics predicted by many other theories within their respective scopes of applicability.

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• Kinetic theory
• Macroscopic fluctuation theory
• Nonequilibrium statistical mechanics
• Liquids
• Second quantization