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

On the rate of change of Varentropy for Markov diffusion processes