Woodchips mulch adds nitrogen to the soil through bacteria in the soil which causes decomposition. It's is a very different substance from wood ash.
When woodchip is placed on the surface of the soil, the slow decomposition of the chips begin forming a microbe-rich ecosystem, Elaine Ingham says this is part of the Soil Food Web. Dcomposition happens when microbial organisms consuming the chips being to produced organisms high in nitrogen and other nutrients that eventually leaches into the soil.
Wood ask is not microbial, it's no longer a living produce. The wood ash question has been answerd.
