  Following work of Colding-Minicozzi, we define a notion of entropy for
connections over $\mathbb R^n$ which has shrinking Yang-Mills solitons as
critical points. As in Colding-Minicozzi, this entropy is defined implicitly,
making it difficult to work with analytically. We prove a theorem
characterizing entropy stability in terms of the spectrum of a certain linear
operator associated to the soliton. This leads furthermore to a gap theorem for
solitons. These results point to a broader strategy of studying "generic
singularities" of Yang-Mills flow, and we discuss the differences in this
strategy in dimension $n=4$ versus $n \geq 5$.
