$u$ is the e&m field energy

$\frac{\partial u}{\partial t}=H\cdot \frac{\partial B}{\partial t}+E\cdot \frac{\partial D}{\partial t}$

Compared with thermo physics: $PdV,TdS,\mu dN$

${H,E,P,T,\mu}$ are intensive variables

${B,D,V,S,N}$ are extensive variables

But in microscopic level, there is no $H$ field. $B$ should be more meaningful.

My question is, why are $H$ and $E$ intensive variable. Why are $D$ and $B$ extensive variables?

I think all of them $E,D,H,B$ should be intensive, because energy density $u$ itself is an intensive variable.