Generalization of the multirate basis for time convolution to unequal forward and reverse rates and connection to reactions with memory

The convolution form used to express mass transfer between mobile and immobile aqueous domains, and often associated with multirate mass transfer representations of matrix diffusion processes, is generalized to the case of unequal forward and reverse rates for each of the multiple rates of the multirate mass transfer and is shown to represent also linear but non-Markovian reactions that kinetically partition mass between mobile and immobile phases with rate of return to mobile phase dependent on contiguous time spent in the immobile phase. In the case where a multirate model refers to multiple sites with distributed mobilization or release rates but single-valued immobilization rate, an equivalent formulation is found using single-site mobilization-immobilization with non-Markovian mobilization rate dependent on contiguous time spent immobilized.