  Relying on the reverse-time space-time harmonic property of the ratio of two
solutions of the Fokker-Plank equation, we establish an explicit formula for
derivative of the \emph{varentropy} for a Markov diffusion process. The formula
involves a nonlinear function of the {\em local free energy}
$\ln(p_t(x)/\bar{p}(x))$.We then verify that our formula yields the correct
result in the simple case of a scalar Gaussian diffusion. In the latter case,
varentropy is exponentially decaying to zero.
