Reaction–subdiffusion equations for the A→B reaction in space- and time-dependent force fields: A study for the anomalous dielectric relaxation

To describe the anomalous dielectric relaxation of reaction in space- and time-dependent electric field, we derive the possible kinetic equations for describing the distributions of A and B particles in a simple reaction A→B based on the biased continuous time random walk, when the jumping probabilities are evaluated after or before the waiting time, respectively. Different reaction—subdiffusion equations are derived for different cases, in which the properties of A and B particles are the same or different. The reaction and subdiffusion terms can be decoupled if the past is forgotten when B particles are converted by A particles. According to the corresponding kinetic equations in the spherical coordinates, the dielectric polarization of the reaction is derived. By comparing the different expressions of the polarization, it is found that the reaction–subdiffusion equation based on the jumping probabilities, which are independent of time and evaluated before the waiting time, is more reasonable to describe the dielectric relaxation process in the chemical reaction.