  I investigate the evolution of finite temperature, classical Yang-Mills field
equations under the influence of a chemical potential for Chern Simons number
$N_{CS}$. The rate of $N_{CS}$ diffusion, $\Gamma_d$, and the linear response
of $N_{CS}$ to a chemical potential, $\Gamma_\mu$, are both computed; the
relation $\Gamma_d = 2 \Gamma_\mu$ is satisfied numerically and the results
agree with the recent measurement of $\Gamma_d$ by Ambjorn and Krasnitz. The
response of $N_{CS}$ under chemical potential remains linear at least to $\mu =
6 T$, which is impossible if there is a free energy barrier to the motion of
$N_{CS}$. The possibility that the result depends on lattice artefacts via hard
thermal loops is investigated by changing the lattice action and by examining
elongated rectangular lattices; provided that the lattice is fine enough, the
result is weakly if at all dependent on the specifics of the cutoff. I also
compare SU(2) with SU(3) and find $\Gamma_{\rm SU(3)} \sim 7
(\alpha_s/\alpha_w)^4 \Gamma_{\rm SU(2)}$.
