  A basic result of large deviations theory is Sanov's theorem, which states
that the sequence of empirical measures of independent and identically
distributed samples satisfies the large deviation principle with rate function
given by relative entropy with respect to the common distribution. Large
deviation principles for the empirical measures are also known to hold for
broad classes of weakly interacting systems. When the interaction through the
empirical measure corresponds to an absolutely continuous change of measure,
the rate function can be expressed as relative entropy of a distribution with
respect to the law of the McKean-Vlasov limit with measure-variable frozen at
that distribution. We discuss situations, beyond that of tilted distributions,
in which a large deviation principle holds with rate function in relative
entropy form.
