High temperature color conductivity at next-to-leading log order

The non-Abelian analogue of electrical conductivity at high temperature has previously been known only at leading logarithmic order - that is, neglecting effects suppressed only by an inverse logarithm of the gauge coupling. We calculate the first sub-leading correction. This has immediate application to improving, to next-to-leading log order, both effective theories of non-perturbative color dynamics, and calculations of the hot electroweak baryon number violation rate.