  The soft radiation emitted in jet cross sections can resolve the directions
and colors of individual hard partons, leading to a complicated pattern of
logarithmically enhanced terms in the perturbative series. Starting from a
factorization theorem and solving the renormalization group equations for its
ingredients, these large logarithms can be resummed. In this paper, we extract
the two-loop anomalous dimension governing the resummation of subleading
logarithms in jet cross sections and other non-global observables. This
anomalous dimension can be obtained by considering soft limits of hard
amplitudes, but the presence of collinear singularities in intermediate
expressions makes its extraction delicate. As a consistency check, we use our
results to predict the known subleading non-global logarithms in the two-jet
cross section.
