Supplementary Material

To make a better comparison of the influence of lattice topological properties on thermalization processes across different systems，in the main text, we deliberately controlled the excitation conditions in two distinct energy bands (subsystems). Specifically, both subsystems were excited with the same number of consecutive modes with homogeneous power. These configurations ensure that the two subsystems maintain comparable prethermalized states. Here, we present a concise introduction to the thermalization process in systems where the excitations exhibit significant disparity between the upper and lower energy bands (subsystems).