If you consider two probability distributions $p$ and $q$, one way to measure the distance between the two is the Kullback-Leibler divergence:

$$KL(p,q)=\int p \log (p/q) = E_p(\log p/q)$$

and this has many good properties.

I'm currently writing an article in which I want to use what I call the KL variance:

$$KL_{var}(p,q) = var_p(\log p/q) = \int p \log^2 (p/q) - KL(p,q)^2$$

Which also has many good properties

I have searched around quite a bit for references to this divergence, and I haven't found anything. Does anybody have an existing reference to this divergence ? Are there any names which would be slightly more catchy than KL-variance?