I investigate the evolution of finite temperature, classical Yang-Mills field equations under the influence of a chemical potential for Chern-Simons number N C S . The rate of N C S diffusion, Γ d , and the linear response of N C S to a chemical potential, Γ μ , are both computed; the relation Γ d = 2 Γ μ is satisfied numerically and the results agree with the recent measurement of Γ d by Ambj rn and Krasnitz. The response of N C S under chemical potential remains linear at least to μ = 6T, which is impossible if there is a free energy barrier to the motion of N C S . 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 Γ S U ( 3 ) 7(α s /α w ) 4 Γ S U ( 2 ) .