Exact Analytic Solution of the Non-Markovian Chemical Reaction Process Via Time-Subordination

Abstract:

Perfectly-mixed reactions are Markovian, because the advance of the state depends only on the current state. Poor mixing (or the partner process of upscaling over heterogeneous concentrations) renders the process non-Markovian because of memory of the chemical structure. In other words, a particle takes some time to reach a suitable reaction site. The time depends on structure, and the structure changes over time. For purely diffusive transport, a calculation of the random time to reach the edges of ``islands’’ allows a solution of the non-Markovian reaction rates that evolve (decrease) over time. This randomization of the active (operational) reaction time leads to non-Markovian reactions and an integro-differential governing equation of chemical evolution. Implications for more complex (advection/diffusion) environments are discussed.