We study numerically a dynamic scaling of a diffusion process involving the Langmuir type adsorption. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations. We study further the dynamic scaling law on fractal surfaces. The adsorption-diffusion process obeys the fracton dynamics on the fractal surfaces.

Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning entanglement of a subsystem can be expressed as sum terms scale linearly with its volume and area, plus correction term is independent size. We conjecture these have efficient dual description set marginal density matrices on bounded regions, obeying the same law locally. prove restricted versi...