Renormalized chemical kinetics: a wave equation encoding the time and temperature evolution of reaction rate processes

Chemical kinetics treats time and temperature as variables, often considered decoupled: both are effectively operating in approaches to reactivity, from elementary processes to complex reactive systems. This work extends a recently introduced renormalization approach based on reactant or product scalar fields (simple or lumped), evolving in both time and (reciprocal) temperature, governed by a system of coupled first order partial differential equations: under isothermal constraint, equivalence is here shown to a wave equation. The transitivity function, central to our formalism, defined as the reciprocal of the apparent activation energy, mediates the coupling between temporal dynamics and thermal dependence; the concept of reaction order is generalized to non-integer values: enforcing continuous symmetry reduction and variable transformations, a general partial differential wave equation and its solutions are obtained and traveling wave profiles are illustrated. Idealized conditions for experimental versus simulation interplay are sketched, relevant for basic elementary or lumped restricted processes. Applications are indicated for the disentangling of complex mechanisms that involve time–temperature coupling. Extension of the wave equation to include key ingredients required by rescaling protocol, are indicated to promote further understanding of the effective coupling parameters under renormalization invariance. Graphical Abstract