he canonical divergence D induces the metric g and the connections∇and∇∗. The same holds for the mean canonical divergence D∇mcd

if∇is integrable, then it is notgenerally true that X(q,p) =−gradqD∇mcd(p‖·)

mean canonical divergenceD∇mcd(p‖q):=12(D(p‖q) +D∗(q‖p))(64)which obviously satisfiesD(∇∗)mcd(p‖q) =D∇mcd(q‖p)